kozpub.bib

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\providecommand{\bbljan}[0]{January}
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@ARTICLE{AKKS:DU74:e,
 author        = "Ahmerov, R. R. and Kamenski{\u\i}, M. I. and Kozjakin, V. S.
                  and Sobolev, A. V.",
 title         = "Periodic solutions of systems of autonomous
                  functional-differential equations of neutral type with
                  small lag",
 journal       = "Differ. Uravn.",
 fjournal      = "Differencial'nye Uravnenija",
 year          = "1974",
 volume        = "10",
 number        = "11",
 pages         = "1923--1931, 2081",
 issn          = "0374-0641",
 mrclass       = "34K15",
 mrnumber      = "0367402 (51 \#3644)",
 mrreviewer    = "G. B. Gustafson",
 zblnumber     = "0292.34074",
 language      = "english",
}

@ARTICLE{NDKKP:DSS96,
 author        = "Al-Nayef, A. and Diamond, P. and Kloeden, P. and Kozyakin,
                  V. and Pokrovskii, A.",
 title         = "Bi-shadowing and delay equations",
 journal       = "Dynam. Stability Systems",
 fjournal      = "Dynamics and Stability of Systems. An International
                  Journal",
 year          = "1996",
 volume        = "11",
 number        = "2",
 pages         = "121--134",
 issn          = "0268-1110",
 mrclass       = "34K15 (34G10)",
 mrnumber      = "1396892 (97f:34045)",
 mrreviewer    = "Xiao Xin Liao",
 zblnumber     = "0854.34064",
 doi           = "10.1080/02681119608806220",
 url           = "https://www.tandfonline.com/doi/abs/10.1080/02681119608806220",
 language      = "english",
 annote        = "The concept of bi-shadowing comes in two parts: direct
                  shadowing in which there is some true trajectory near a
                  given pseudo-trajectory; and indirect or inverse shadowing
                  in which there is some pseudo-trajectory near a given true
                  trajectory. Shadowing results typically establish only
                  direct shadowing and involve rather stringent assumptions
                  such as that the dynamical system is generated by a
                  hyperbolic diffeomorphism. Many useful properties of
                  hyperbolic diffeomorphisms are retained by the
                  semi-hyperbolic mappings. Here it will be shown that
                  semi-hyperbolicity of a Lipschitz mapping on a given set
                  implies bi-shadowing for a wide class of dynamical systems
                  in infinite dimensional Banach spaces.",
}

@ARTICLE{Obituary:JAMSA97,
 author        = "Asarin, E. A. and Bakhtin, I. A. and Bobylev, N. A. and
                  Bondarenko, V. A. and Burd, V. {\relax{}Sh}. and
                  Chernorutskii, V. V. and Gorin, E. A. and Kozyakin, V. S.
                  and Krasnosel'skii, A. M. and Kurzhanskii, A. B. and
                  Kuznetsov, N. A. and Levin, A. {\relax{}Yu}. and
                  Mukhamadiev, E. M. and Perov, A. I. and Pokorny,
                  {\relax{}Yu}. V. and Pokrovskii, A. V. and Rachinskii, D.
                  I. and Sadovsky, B. N. and Strygin, V. V. and Tsypkin,
                  {\relax{}Ya}. Z. and Yemel'yanov, S. V. and Zabreiko, P.
                  P.",
 title         = "{M}ark {A}lexandrovich {K}rasnosel'skii ({A}pril 27,
                  1920--{F}ebruary 13, 1997)",
 journal       = "J. Appl. Math. Stochastic Anal.",
 fjournal      = "Journal of Applied Mathematics and Stochastic Analysis",
 year          = "1997",
 volume        = "10",
 number        = "2",
 pages         = "119--126",
 issn          = "1048-9533",
 mrnumber      = "1453463",
 zblnumber     = "0880.01008",
 language      = "english",
 annote        = "On February 13, 1997, the world famous mathematician, Mark
                  Alexandrovich Krasnosel'skii, died unexpectedly. This
                  article gives a brief overview of his life and research.",
}

@BOOK{AKKK:92:e,
 author        = "Asarin, E. A. and Kozyakin, V. S. and Krasnosel'ski{\u\i},
                  M. A. and Kuznetsov, N. A.",
 title         = "Analiz ustoichivosti rassinkhronizovannykh diskretnykh
                  sistem",
 publisher     = "Nauka",
 address       = "Moscow",
 year          = "1992",
 pages         = "408",
 isbn          = "5-02-006946-9",
 mrclass       = "93D05 (39A11)",
 mrnumber      = "1693324",
 doi           = "10.13140/RG.2.1.3381.6169",
 url           = "http://eqworld.ipmnet.ru/ru/library/books/AsarinKozyakinKrasnoselskijKuznecov1992ru.pdf",
 language      = "english",
 note          = "In Russian",
 annote        = "Control systems with asynchronous data exchange are
                  considered. The stability theory of such systems (for
                  various desynchronization classes) is presented. Some
                  results may be considered as a new chapter of the theory of
                  matrices. The correctness of the proposed models is also
                  investigated. Many open problems are set forth. For
                  engineers, mathematicians and control theorists. In
                  Russian.",
}

@ARTICLE{AKKK:MCM90,
 author        = "Asarin, E. A. and Krasnoselskii, M. A. and Kozyakin, V. S.
                  and Kuznetsov, N. A.",
 title         = "On modelling systems with non-synchronously operating
                  impulse elements",
 journal       = "Math. Comput. Model.",
 fjournal      = "Mathematical and Computer Modelling",
 year          = "1990",
 volume        = "14",
 number        = "C",
 pages         = "70--73",
 zblnumber     = "0744.93082",
 zblreviewer   = "E. Eitelberg (Durban)",
 doi           = "10.1016/0895-7177(90)90149-H",
 url           = "https://www.sciencedirect.com/science/article/pii/089571779090149H",
 language      = "english",
 annote        = "Systems with impulse elements operating by some reason
                  non-synchronously are often used in control science,
                  technic, economics, ecology etc. To analyze such
                  desynchronized systems one needs new constructions. Some
                  results connected with new models and computer methods of
                  stability analysis are set forth. The methods of stability
                  analysis of synchronized systems are well developed. As a
                  computer experiment has demonstrated all the conceivable
                  effects of synchronized systems loosing, gaining or
                  conserving stability are possible. So desynchronized
                  systems require the development of special methods of
                  stability analysis. In some simple cases the conditions of
                  stability can be expressed by formulae. In other situations
                  numerical methods of stability analysis of desynchronized
                  systems are to be developed. Three situations of this kind
                  are discussed in detail. 1. Phase and frequency
                  desynchronized systems, i.e. linear systems with
                  periodically switched components are considered. 2. It is
                  discussed, what is to be done if a system is sensitive to
                  desynchronization (looses stability under
                  desynchronization). A method to do away with such a
                  sensitivity is proposed. 3. Stochastically desynchronized
                  systems are considered.",
}

@ARTICLE{AKKK:IFAC90,
 author        = "Asarin, E. A. and Krasnoselskii, M. A. and Kozyakin, V. S.
                  and Kuznetsov, N. A.",
 title         = "Stability analysis of desynchronized systems",
 journal       = "IFAC Proceedings Volumes",
 year          = "1990",
 volume        = "23",
 number        = "8, Part 1",
 pages         = "117--121",
 keywords      = "mathematical system theory; stability; discrete time
                  systems; stochastic systems; linear systems",
 issn          = "1474-6670",
 doi           = "10.1016/S1474-6670(17)52081-9",
 url           = "https://www.sciencedirect.com/science/article/pii/S1474667017520819",
 language      = "english",
 note          = "11th IFAC World Congress on Automatic Control, Tallinn, 1990
                  -- Volume 1, Tallinn, Finland",
 annote        = "Multi-component systems consisting of components working at
                  discrete time instants are considered. It is supposed that
                  instants of different components functioning do not always
                  coincide. Such systems are referred to as desynchronized.
                  Multi-processor systems and computer systems with
                  asynchronous computations may serve as typical examples.
                  The influence of instants of components acting over the
                  system stability is studied. Three situations,
                  substantially differing by both methods and results of
                  investigation, are considered. The former deals with the
                  case when the system's components work periodically, the
                  periods in general not coinciding. The second situation
                  embraces the case when the components switching instants
                  are random. The latter situation concerns the case when we
                  know nothing about laws describing instants of components
                  work. The results of the investigation demonstrate that the
                  type of desynchronization can essentially affect the
                  dynamics of the system. Sometimes desynchronized systems
                  possess some properties not possessed by synchronized
                  systems.",
}

@MISC{ACDDHK15,
 author        = "Asarin, Eugene and Cervelle, Julien and Degorre, Aldric and
                  Dima, Catalin and Horn, Florian and Kozyakin, Victor",
 title         = "Entropy Games and Matrix Multiplication Games",
 howpublished  = "ArXiv.org e-Print archive",
 year          = "2015",
 month         = jun,
 keywords      = "entropy; joint spectral radius; game theory",
 eprinttype    = "arXiv",
 eprint        = "1506.04885",
 hal_id        = "hal-01164086",
 hal_version   = "v1",
 doi           = "10.48550/arXiv.1506.04885",
 language      = "english",
 annote        = "An entropy game is played on a finite arena by
                  two-and-a-half players: Despot, Tribune and
                  non-deterministic People. Whenever Despot and Tribune
                  decide of their actions, it remains a set L of possible
                  behaviors of People. Despot aims the entropy (growth rate)
                  of L to be as small as possible, while Tribune wants to
                  make it as large as possible. The main result is that the
                  entropy game is determined, and that the optimal strategies
                  for Despot and Tribune are positional. The analysis is
                  based on that of matrix multiplication games, also novel
                  and generalizing the theory of joint spectral radius.",
}

@INPROCEEDINGS{ACDDHK:STACS15,
 author        = "Asarin, Eugene and Cervelle, Julien and Degorre, Aldric and
                  Dima, Catalin and Horn, Florian and Kozyakin, Victor",
 editor        = "Ollinger, Nicolas and Vollmer, Heribert",
 title         = "Entropy Games and Matrix Multiplication Games",
 booktitle     = "33rd Symposium on Theoretical Aspects of Computer Science,
                  (STACS 2016)",
 series        = "LIPIcs. Leibniz Int. Proc. Inform.",
 publisher     = "Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik",
 address       = "Dagstuhl, Germany",
 year          = "2016",
 volume        = "47",
 pages         = "11:1--11:14",
 keywords      = "game theory; entropy; joint spectral; radius",
 isbn          = "978-3-95977-001-9",
 issn          = "1868-8969",
 mrclass       = "91A10 (15A99 68Q25)",
 mrnumber      = "3539108",
 zblnumber     = "1390.91016",
 doi           = "10.4230/LIPIcs.STACS.2016.11",
 url           = "https://drops.dagstuhl.de/opus/volltexte/2016/5712/",
 language      = "english",
 annote        = "Two intimately related new classes of games are introduced
                  and studied: entropy games (EGs) and matrix multiplication
                  games (MMGs). An EG is played on a finite arena by
                  two-and-a-half players: Despot, Tribune and the
                  non-deterministic People. Despot wants to make the set of
                  possible People's behaviors as small as possible, while
                  Tribune wants to make it as large as possible. An MMG is
                  played by two players that alternately write matrices from
                  some predefined finite sets. One wants to maximize the
                  growth rate of the product, and the other to minimize it.
                  We show that in general MMGs are undecidable in quite a
                  strong sense. On the positive side, EGs correspond to a
                  subclass of MMGs, and we prove that such MMGs and EGs are
                  determined, and that the optimal strategies are simple. The
                  complexity of solving such games is in NP cap coNP.",
}

@INCOLLECTION{AKKKP:88,
 author        = "Asarin, {\relax{}Ye}. A. and Kozyakin, V. S. and
                  Krasnosel'skii, M. A. and Kuznetsov, N. A. and Pokrovskii,
                  A. V.",
 title         = "On some new types of mathematical models of complex
                  systems",
 booktitle     = "Modelling and adaptive control ({S}opron, 1986)",
 series        = "Lecture Notes in Control and Inform. Sci.",
 publisher     = "Springer",
 address       = "Berlin",
 year          = "1988",
 volume        = "105",
 pages         = "10--26",
 mrclass       = "93A10 (93C55 93D20)",
 mrnumber      = "958694",
 zblnumber     = "0648.93025",
 zblreviewer   = "A. Van{\v{e}}{\v{c}}ek",
 doi           = "10.1007/BFb0043174",
 url           = "https://link.springer.com/chapter/10.1007/BFb0043174",
 language      = "english",
 annote        = "The paper is aimed at consideration of two new models whose
                  study has just begun. Desynchronized linear models are
                  introduced as discrete linear models with the state
                  coordinates changing at different times. Desynchronization
                  is suggested as the easiest way to attain stability for
                  some systems. Moreover, the limit hysteresis nonlinearities
                  are introduced and the averaging principle is studied.",
}

@INPROCEEDINGS{BKK95,
 author        = "Bhaya, Amit and Kaszkurewicz, Eugenius and Kozyakin, V. S.",
 title         = "Existence and Stability of a Unique Equilibrium in
                  Continuous-Valued Discrete-Time Asynchronous {H}opfield
                  Neural Networks",
 booktitle     = "Proceedings of 1995 IEEE International Symposium on Circuits
                  and Systems. ISCAS'95",
 year          = "1995",
 volume        = "2",
 pages         = "1140--1143",
 doi           = "10.1109/ISCAS.1995.520345",
 url           = "https://ieeexplore.ieee.org/document/520345",
 language      = "english",
 annote        = "This paper investigates a continuous-valued discrete-time
                  analog of the well-known continuous-valued continuous-time
                  Hopfield neural network model, first proposed by Takeda and
                  Goodman (1986). It is shown that the assumption of
                  D-stability of the interconnection matrix, together with
                  the standard assumptions on the activation functions,
                  guarantee the existence of a unique equilibrium under a
                  synchronous mode of operation as well as a class of
                  asynchronous modes. Conditions for local and global
                  asymptotic stability are also derived, for both synchronous
                  and asynchronous modes of operation. The results obtained
                  are discussed both from the points of view of applications
                  and robustness.",
}

@ARTICLE{BKK:IEEETNN96,
 author        = "Bhaya, Amit and Kaszkurewicz, Eugenius and Kozyakin, V. S.",
 title         = "Existence and stability of a unique equilibrium in
                  continuous-valued discrete-time asynchronous {H}opfield
                  neural networks",
 journal       = "IEEE Trans. Neural Netw.",
 fjournal      = "IEEE Transactions on Neural Networks",
 year          = "1996",
 volume        = "7",
 number        = "3",
 pages         = "620--628",
 month         = may,
 issn          = "1045-9227",
 doi           = "10.1109/72.501720",
 url           = "https://ieeexplore.ieee.org/document/501720",
 language      = "english",
 annote        = "It is shown that the assumption of $D$-stability of the
                  interconnection matrix, together with the standard
                  assumptions on the activation functions, guarantee the
                  existence of a unique equilibrium under a synchronous mode
                  of operation as well as a class of asynchronous modes. For
                  the synchronous mode, these assumptions are also shown to
                  imply local asymptotic stability of the equilibrium. For
                  the asynchronous mode of operation, two results are
                  derived. First, it is shown that symmetry and stability of
                  the interconnection matrix guarantee local asymptotic
                  stability of the equilibrium under a class of asynchronous
                  modes-this is referred to as local absolute asymptotic
                  stability. Second, it is shown that, under the standard
                  assumptions, if the nonnegative matrix whose elements are
                  the absolute values of the corresponding elements of the
                  interconnection matrix is stable, then the equilibrium is
                  globally absolutely asymptotically stable under a class of
                  asynchronous modes. The results obtained are discussed from
                  the points of view of their applications, robustness, and
                  their relationship to earlier results.",
}

@BOOK{MTS:86:e,
 author        = "Bobyl{\"e}v, N. A. and Boltyanski{\u\i}, V. G. and
                  Vsekhsvyatski{\u\i}, S. {\relax{}Yu}. and Kalashnikov, V.
                  V. and Kozyakin, V. S. and Kolmanovski{\u\i}, V. B. and
                  Kravchenko, A. A. and Krasnosel'ski{\u\i}, A. M. and
                  Pokrovski{\u\i}, A. V.",
 title         = "Matematicheskaya teoriya sistem",
 publisher     = "Nauka",
 address       = "Moscow",
 year          = "1986",
 pages         = "166",
 mrclass       = "93-02 (49-02 49B10)",
 mrnumber      = "862446 (88a:93001)",
 mrreviewer    = "V. Popescu",
 language      = "english",
 note          = "In Russian",
 annote        = "The book presents a number of chapters of modern
                  mathematical theory of systems. Methods for solving
                  optimization problems for various classes of systems are
                  considered. Much attention is paid to methods for studying
                  the dynamics of processes in general nonlinear systems and
                  systems with non-standard links; methods for the
                  approximate construction of solutions and the possibility
                  of simplifying the corresponding equations are studied;
                  properties of stochastic models are investigated.\par For
                  specialists in the theory of systems, control theory,
                  mathematicians, mechanics.",
}

@ARTICLE{BKPS:JAMSA97,
 author        = "Bobylev, Nikolai A. and Kozyakin, Victor S. and Pokrovskii,
                  Alexei V. and Sadovskii, Boris N.",
 title         = "Obituary: {M}ark {A}lexandrovich {K}rasnosel'skii ({A}pril
                  27, 1920--{F}ebruary 13, 1997)",
 journal       = "J. Appl. Math. Stochastic Anal.",
 fjournal      = "Journal of Applied Mathematics and Stochastic Analysis",
 year          = "1997",
 volume        = "10",
 number        = "1",
 pages         = "1",
 issn          = "1048-9533",
 mrclass       = "01A70",
 mrnumber      = "1437947",
 doi           = "10.1155/S1048953397000014",
 url           = "https://www.hindawi.com/journals/ijsa/1997/637327/abs/",
 language      = "english",
 annote        = "One of the founders of nonlinear functional analysis, Mark
                  Alexandrovich Krasnosel'skii, passed away at the age of 77
                  working at his desk in his Moscow flat on February 13. He
                  was the author of hundreds of papers (including a good
                  dozen in 1996) and twelve research monographs translated
                  into many languages. Mark Krasnosel'skii had amazingly
                  broad scientific interests; his work opened new horizons in
                  classical functional analysis, oscillation theory,
                  numerical methods, variational problems, the mathematical
                  theory of hysteresis and other areas. He was a superb
                  teacher, an energetic scientific organizer and the creator
                  of a mathematical school known worldwide. More that a
                  hundred of his students are now working in different areas
                  of pure and applied mathematics all over the world.\par
                  Mark Krasnosel'skii had a distinguished personality:
                  straightforward and uncompromising in matters of principle
                  but always open-minded and ready to help anyone. He was an
                  indefatigable hard worker. The driving energy of Mark
                  Krasnosel'skii inspired his colleagues and students. A big
                  man and great mathematician left this world. His life and
                  his scientific achievements will take some time to fully
                  appreciate. We are saddened at the loss of our much beloved
                  teacher and express our sympathy to his large family.",
}

@TECHREPORT{CrossKoz12,
 author        = "Cross, Rod and Kozyakin, Victor",
 title         = "Fact and Fiction in {FX} Arbitrage Processes",
 institution   = "University of Strathclyde Business School, Department of
                  Economics",
 year          = "2012",
 number        = "1211",
 type          = "Working Papers",
 month         = jul,
 keywords      = "triangular arbitrage; fx markets; periodic sequences;
                  asynchronous systems; the fear index",
 url           = "https://ideas.repec.org/p/str/wpaper/1211.html",
 language      = "english",
 annote        = "The efficient markets hypothesis implies that arbitrage
                  opportunities in markets such as those for foreign exchange
                  (FX) would be, at most, short-lived. The present paper
                  surveys the fragmented nature of FX markets, revealing that
                  information in these markets is also likely to be
                  fragmented. The ``quant'' workforce in the hedge fund
                  featured in The Fear Index novel by Robert Harris would
                  have little or no reason for their existence in an EMH
                  world. The four currency combinatorial analysis of
                  arbitrage sequences contained in Cross, Kozyakin,
                  O'Callaghan, Pokrovskii and Pokrovskiy (2012) is then
                  considered. Their results suggest that arbitrage processes,
                  rather than being self-extinguishing, tend to be periodic
                  in nature. This helps explain the fact that arbitrage
                  dealing tends to be endemic in FX markets.",
}

@TECHREPORT{CrossKoz14,
 author        = "Cross, Rod and Kozyakin, Victor",
 title         = "Fact and Fiction in {FX} Arbitrage Processes",
 institution   = "University of Strathclyde",
 year          = "2014",
 number        = "SIRE-DP-2014-003",
 type          = "SIRE Discussion Paper",
 month         = mar,
 keywords      = "triangular arbitrage; fx markets; periodic sequences;
                  asynchronous systems; the fear index",
 url           = "https://ideas.repec.org/p/edn/sirdps/563.html",
 language      = "english",
 annote        = "The efficient markets hypothesis implies that arbitrage
                  opportunities in markets such as those for foreign exchange
                  (FX) would be, at most, short-lived. The present paper
                  surveys the fragmented nature of FX markets, revealing that
                  information in these markets is also likely to be
                  fragmented. The ``quant'' workforce in the hedge fund
                  featured in The Fear Index novel by Robert Harris would
                  have little or no reason for their existence in an EMH
                  world. The four currency combinatorial analysis of
                  arbitrage sequences contained in Cross, Kozyakin,
                  O'Callaghan, Pokrovskii and Pokrovskiy (2012) is then
                  considered. Their results suggest that arbitrage processes,
                  rather than being self-extinguishing, tend to be periodic
                  in nature. This helps explain the fact that arbitrage
                  dealing tends to be endemic in FX markets.",
}

@ARTICLE{CrossKoz:JPCS15,
 author        = "Cross, Rod and Kozyakin, Victor",
 title         = "Fact and fictions in {FX} arbitrage processes",
 journal       = "J. Phys.: Conf. Ser.",
 year          = "2015",
 volume        = "585",
 number        = "012015",
 keywords      = "triangular arbitrage; fx markets; periodic sequences;
                  asynchronous systems; the fear index",
 doi           = "10.1088/1742-6596/585/1/012015",
 url           = "https://iopscience.iop.org/article/10.1088/1742-6596/585/1/012015",
 language      = "english",
 annote        = "The efficient markets hypothesis implies that arbitrage
                  opportunities in markets such as those for foreign exchange
                  (FX) would be, at most, short-lived. The present paper
                  surveys the fragmented nature of FX markets, revealing that
                  information in these markets is also likely to be
                  fragmented. The ``quant'' workforce in the hedge fund
                  featured in \emph{The Fear Index} novel by Robert Harris
                  would have little or no reason for their existence in an
                  EMH world. The four currency combinatorial analysis of
                  arbitrage sequences contained in Cross, Kozyakin,
                  O'Callaghan, Pokrovskii and Pokrovskiy (2012) is then
                  considered. Their results suggest that arbitrage processes,
                  rather than being self-extinguishing, tend to be periodic
                  in nature. This helps explain the fact that arbitrage
                  dealing tends to be endemic in FX markets.",
}

@ARTICLE{CrossKPP:MECA12,
 author        = "Cross, Rod and Kozyakin, Victor and O'Callaghan, Brian and
                  Pokrovskii, Alexei and Pokrovskiy, Alexey",
 title         = "Periodic Sequences of Arbitrage: A Tale of Four Currencies",
 journal       = "Metroeconomica",
 year          = "2012",
 volume        = "63",
 number        = "2",
 pages         = "250--294",
 month         = may,
 eprinttype    = "arXiv",
 eprint        = "1112.5850",
 zblnumber     = "1242.91152",
 doi           = "10.1111/j.1467-999X.2011.04140.x",
 url           = "https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1467-999X.2011.04140.x",
 language      = "english",
 annote        = "This paper investigates arbitrage chains involving four
                  currencies and four foreign exchange trader-arbitrageurs.
                  In contrast with the three-currency case, we find that
                  arbitrage operations when four currencies are present may
                  appear periodic in nature, and not involve smooth
                  convergence to a `balanced' ensemble of exchange rates in
                  which the law of one price holds. The goal of this article
                  is to understand some interesting features of sequences of
                  arbitrage operations, features of which might well be
                  relevant in other contexts in finance and economics.",
}

@ARTICLE{CrossKoz:DCDSB13,
 author        = "Cross, Rod and Kozyakin, Victor S.",
 title         = "Double exponential instability of triangular arbitrage
                  systems",
 journal       = "Discrete Contin. Dyn. Syst. Ser. B",
 fjournal      = "Discrete and Continuous Dynamical Systems. Series B. A
                  Journal Bridging Mathematics and Sciences",
 year          = "2013",
 volume        = "18",
 number        = "2",
 pages         = "349--376",
 eprinttype    = "arXiv",
 eprint        = "1204.3422",
 issn          = "1531-3492",
 mrclass       = "91G80",
 mrnumber      = "2999081",
 zblnumber     = "1260.91261",
 doi           = "10.3934/dcdsb.2013.18.349",
 url           = "https://www.aimsciences.org/article/doi/10.3934/dcdsb.2013.18.349",
 language      = "english",
 annote        = "If financial markets displayed the informational efficiency
                  postulated in the efficient markets hypothesis (EMH),
                  arbitrage operations would be self-extinguishing. The
                  present paper considers arbitrage sequences in foreign
                  exchange (FX) markets, in which trading platforms and
                  information are fragmented. In [\emph{R. Cross} et al.,
                  Metroeconomica 63, No. 2, 250--294] it was shown that
                  sequences of triangular arbitrage operations in FX markets
                  containing 4 currencies and trader-arbitrageurs tend to
                  display periodicity or grow exponentially rather than being
                  self-extinguishing. This paper extends the analysis to 5 or
                  higher-order currency worlds. The key findings are that in
                  a 5-currency world arbitrage sequences may also follow an
                  exponential law as well as display periodicity, but that in
                  higher-order currency worlds a double exponential law may
                  additionally apply. There is an ``inheritance of
                  instability'' in the higher-order currency worlds.
                  Profitable arbitrage operations are thus endemic rather
                  that displaying the self-extinguishing properties implied
                  by the EMH.",
}

@ARTICLE{DK:INFOPROC11:e,
 author        = "Dai, Xiongping and Kozyakin, Victor",
 title         = "Finiteness Property of a Bounded Set of Matrices with
                  Uniformly Sub-Peripheral Spectrum",
 journal       = "J. Commun. Technol. Electron.",
 fjournal      = "Journal of Communications Technology and Electronics",
 year          = "2011",
 volume        = "56",
 number        = "12",
 pages         = "1564--1569",
 eprinttype    = "arXiv",
 eprint        = "1106.2298",
 doi           = "10.1134/S1064226911120096",
 url           = "https://link.springer.com/article/10.1134/S1064226911120096",
 language      = "english",
 annote        = "In the paper, a simple condition guaranteing the finiteness,
                  property, for a bounded set $\boldsymbol{S}=\{S_k\}_{k\in
                  K}$ of real or complex $d\times d$ matrices, is presented.
                  It is, shown that existence of a sequence of matrix
                  products $\boldsymbol{S}_{\!{\sigma(n_{\ell})}}$ of length
                  $n_\ell$ for $\boldsymbol{S}$ with $n_{\ell}\to\infty$ such
                  that the spectrum of each matrix
                  $\boldsymbol{S}_{\!{\sigma(n_{\ell})}}$ is uniformly
                  sub-peripheral and
                  \[{\rho}({\boldsymbol{S}}):=\sup_{n\ge1}\sup_{i_1,\dotsc,i_n\in
                  K} \sqrt[n]{{\rho(S_{i_1}\dotsm
                  S_{i_n})}}=\lim_{\ell\to+\infty}
                  \sqrt[\uproot{3}n_{\ell}]{\rho(\boldsymbol{S}_{\!{\sigma(n_{\ell})}})},
                  \] guarantees the spectral finiteness property for
                  $\boldsymbol{S}$.",
}

@ARTICLE{DKKKP:AIT95:e,
 author        = "Dajmond, F. and Cloeden, P. and Kozyakin, V. S. and
                  Krasnosel'skij, M. A. and Pokrovskij, A. V.",
 title         = "Periodic trajectories of nonsmooth perturbations in chaotic
                  systems",
 journal       = "Autom. Remote Control",
 fjournal      = "Automation and Remote Control",
 year          = "1995",
 volume        = "56",
 number        = "5",
 pages         = "637--643",
 issn          = "0005-1179",
 mrclass       = "58F30 (58F22)",
 mrnumber      = "1346113 (96g:58169)",
 mrreviewer    = "Katarina Jankova",
 zblnumber     = "0917.93029",
 language      = "english",
 annote        = "Periodic modes of complex pseudo-chaotic systems perturbed
                  by small nonsmooth perturbations are investigated under the
                  assumption that the initial system is almost semihyperbolic
                  in the sense of the traditional concept of hyperbolicity.",
}

@TECHREPORT{KKP:CADSEM96-002,
 author        = "Diamond, P. and Kloeden, P. E. and Kozyakin, V. S. and
                  Pokrovskii, A. V.",
 title         = "A phenomenological model for discretizations of chaotic
                  dynamical systems",
 institution   = "Deakin University",
 address       = "Geelong, Australia",
 year          = "1996",
 number        = "96--002",
 pagetotal     = "35",
 type          = "CADSEM Report",
 doi           = "10.13140/RG.2.2.33343.71840",
 language      = "english",
 annote        = "Computer simulations of dynamical systems contain
                  discretizations, where finite machine arithmetic replaces
                  continuum state space. For chaotic dynamical systems, the
                  main features of this discretization are stochastically
                  related to the parameters both of the underlying continuous
                  system and of the computer arithmetic. A model of this
                  process is required to describe and analyze its statistical
                  properties and this is carried out for the family of
                  mappings $f_{\ell}(x) = 1 - |1 - 2x|^{\ell}$, $x\in[0,1]$,
                  $\ell>2$. Computer modeling results are presented.",
}

@ARTICLE{DKKP:MCS97,
 author        = "Diamond, P. and Kloeden, P. E. and Kozyakin, V. S. and
                  Pokrovskii, A. V.",
 title         = "A model for roundoff and collapse in computation of chaotic
                  dynamical systems",
 journal       = "Math. Comput. Simulation",
 fjournal      = "Mathematics and Computers in Simulation",
 year          = "1997",
 volume        = "44",
 number        = "2",
 pages         = "163--185",
 coden         = "MCSIDR",
 issn          = "0378-4754",
 mrclass       = "58F13 (34C35 58F12 65C20 65L20)",
 mrnumber      = "1481914 (99a:58114)",
 mrreviewer    = "T. Erber",
 zblnumber     = "1017.37501",
 doi           = "10.1016/S0378-4754(97)00070-0",
 url           = "https://www.sciencedirect.com/science/article/pii/S0378475497000700",
 language      = "english",
 annote        = "Computer simulations of dynamical systems contain
                  discretizations, where finite machine arithmetic replaces
                  continuum state space. For chaotic dynamical systems, the
                  main features of this discretization are stochastically
                  related to the parameters both, of the underlying
                  continuous system and of the computer arithmetic. A model
                  of this process is required to describe and analyze its
                  statistical properties and this is carried out for the
                  family of mappings $f^{l}(x) = 1 - |1 - 2x|^{l}$, $x \in
                  [0, 1]$, $l > 2$. Computer modeling results are
                  presented.",
}

@TECHREPORT{DKKP:Deakin94,
 author        = "Diamond, P. and Kloeden, P. and Kozyakin, V. and Pokrovskii,
                  A.",
 title         = "Robustness of observed behaviour of semi-hyperbolic
                  dynamical systems",
 institution   = "School of Computing {\&} Mathematics",
 address       = "Deakin University",
 year          = "1994",
 number        = "TR M94/04",
 pages         = "1--14",
 type          = "Technical Reports. Mathematics Series",
 language      = "english",
 annote        = "Computer simulations provide much practical information
                  about the behaviour of specific dynamical systems, though
                  the finiteness of machine arithmetic and the consequent
                  roundoff error that it introduces mean that computed
                  trajectories, or pseudo--trajectories, are really only
                  approximations of actual trajectories of a given dynamical
                  system. The precise relationship between such
                  pseudo--trajectories and the true trajectories is thus of
                  some concern, particularly in chaotic systems with their
                  acute sensitivity to changes in initial conditions. The
                  concept of shadowing attempts to formulate such a
                  relationship and comes in two forms: direct shadowing in
                  which there is some true trajectory near a given
                  pseudo--trajectory; and indirect shadowing in which there
                  is some pseudo--trajectory near a given true trajectory.
                  Shadowing results (cf.[3, 6, 8, 9, 11]) typically establish
                  only direct shadowing and involve rather stringent
                  assumptions such\ldots",
}

@ARTICLE{DKKP:BAMS95,
 author        = "Diamond, P. and Kloeden, P. and Kozyakin, V. and Pokrovskii,
                  A.",
 title         = "Expansivity of semi-hyperbolic {L}ipschitz mappings",
 journal       = "Bull. Austral. Math. Soc.",
 fjournal      = "Bulletin of the Australian Mathematical Society",
 year          = "1995",
 volume        = "51",
 number        = "2",
 pages         = "301--308",
 coden         = "ALNBAB",
 issn          = "0004-9727",
 mrclass       = "58F15 (34C35)",
 mrnumber      = "1322796 (96d:58101)",
 mrreviewer    = "Romeo F. Thomas",
 zblnumber     = "0826.58028",
 doi           = "10.1017/S0004972700014131",
 url           = "https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/expansivity-of-semihyperbolic-lipschitz-mappings/3530D062DB3433AC0CE92841B97CE077",
 language      = "english",
 annote        = "Semi-hyperbolic dynamical systems generated by Lipschitz
                  mappings are shown to be exponentially expansive, locally
                  at least, and explicit rates of expansion are determined.
                  The result is applicable to nonsmooth noninvertible systems
                  such as those with hysteresis effects as well as to
                  classical systems involving hyperbolic diffeomorphisms.",
}

@ARTICLE{DKKP:TCS95,
 author        = "Diamond, P. and Kloeden, P. and Kozyakin, V. and Pokrovskii,
                  A.",
 title         = "On the fragmentary complexity of symbolic sequences",
 journal       = "Theoret. Comput. Sci.",
 fjournal      = "Theoretical Computer Science",
 year          = "1995",
 volume        = "148",
 number        = "1",
 pages         = "1--17",
 coden         = "TCSDI",
 issn          = "0304-3975",
 mrclass       = "68R15 (58F03)",
 mrnumber      = "1347664 (97g:68189)",
 zblnumber     = "0873.68120",
 doi           = "10.1016/0304-3975(94)00261-G",
 url           = "https://www.sciencedirect.com/science/article/pii/030439759400261G",
 language      = "english",
 annote        = "A measure of the ability of a symbolic sequence to be
                  covered by initial fragments of another symbolic sequence
                  is introduced and its basic properties are investigated.
                  Applications to the characterization of symbolic sequences
                  associated with shift mappings on a torus corresponding to
                  a special partitioning of the torus and to multirate
                  systems of coprocessors are considered.",
}

@ARTICLE{DKKP:JNS95,
 author        = "Diamond, P. and Kloeden, P. and Kozyakin, V. and Pokrovskii,
                  A.",
 title         = "Semihyperbolic mappings",
 journal       = "J. Nonlinear Sci.",
 fjournal      = "Journal of Nonlinear Science",
 year          = "1995",
 volume        = "5",
 number        = "5",
 pages         = "419--431",
 issn          = "0938-8974",
 mrclass       = "58F15",
 mrnumber      = "1354569 (96i:58130)",
 mrreviewer    = "Jerzy Ombach",
 zblnumber     = "0855.58044",
 zblreviewer   = "O.-P. Piiril{\"a} (Helsinki)",
 doi           = "10.1007/BF01212908",
 url           = "https://link.springer.com/article/10.1007/BF01212908",
 language      = "english",
 annote        = "Semihyperbolic dynamical systems generated by Lipschitz
                  mappings are investigated. A special form of robustness of
                  topological entropy under perturbations of a Semihyperbolic
                  mapping is discussed, and weakened forms of persistence and
                  of structural stability are considered. Proofs are based on
                  the concept of bi-shadowing, which is a stronger version of
                  the shadowing lemma.",
}

@ARTICLE{DKKKP:NATMA96,
 author        = "Diamond, P. and Kloeden, P. and Kozyakin, V. and
                  Kransnosel'skii, M. and Pokrovskii, A.",
 title         = "Robustness of dynamical systems to a class of nonsmooth
                  perturbations",
 journal       = "Nonlinear Anal.",
 fjournal      = "Nonlinear Analysis. Theory, Methods {\&} Applications. An
                  International Multidisciplinary Journal. Series A: Theory
                  and Methods",
 year          = "1996",
 volume        = "26",
 number        = "2",
 pages         = "351--361",
 coden         = "NOANDD",
 issn          = "0362-546X",
 mrclass       = "47H20 (47H30 58F15)",
 mrnumber      = "1359482 (97d:47077)",
 mrreviewer    = "Wolf-J{\"u}rgen Beyn",
 zblnumber     = "0849.58059",
 doi           = "10.1016/0362-546X(94)00264-I",
 url           = "https://www.sciencedirect.com/science/article/pii/0362546X9400264I",
 language      = "english",
 annote        = "In this paper we apply a recently proposed technique for the
                  analysis of numerical solutions of chaotic systems to
                  analyze a specific class of perturbations which arise in
                  systems with weak hysteresis nonlinearities. An important
                  feature of such models is that hysteresis nonlinearities
                  are treated as continuous but nonsmooth dynamical systems
                  $W$, often with an infinite dimensional set of internal
                  states. This includes such nonlinearities as play, stop,
                  the Besseling-Ishlinskii and Preisach-Giltay models and so
                  on.",
}

@ARTICLE{DKKP:PROCAMS98,
 author        = "Diamond, P. and Kloeden, P. and Kozyakin, V. and Pokrovskii,
                  A.",
 title         = "Monotonic dynamical systems under spatial discretization",
 journal       = "Proc. Amer. Math. Soc.",
 fjournal      = "Proceedings of the American Mathematical Society",
 year          = "1998",
 volume        = "126",
 number        = "7",
 pages         = "2169--2174",
 coden         = "PAMYAR",
 issn          = "0002-9939",
 mrclass       = "58F08",
 mrnumber      = "1443379 (98h:58100)",
 mrreviewer    = "Hal Leslie Smith",
 zblnumber     = "0903.58017",
 zblreviewer   = "S. L. Kalpazidou (Thessaloniki)",
 doi           = "10.1090/S0002-9939-98-04277-4",
 url           = "https://www.ams.org/journals/proc/1998-126-07/S0002-9939-98-04277-4/",
 language      = "english",
 annote        = "We estimate the probability of replicating the asymptotic
                  behaviour of a dynamical system generated by a monotonic
                  mapping for randomly centered roundoff lattices.",
}

@ARTICLE{DKKKP:DAN95:e,
 author        = "Diamond, P. and Kloeden, P. and Kozyakin, V. S. and
                  Krasnosel'skij, M. A. and Pokrovskij, A. V.",
 title         = "Roughness of trajectories of dynamical systems with respect
                  to hysteresis disturbances",
 journal       = "Dokl. Math.",
 fjournal      = "Doklady Mathematics",
 year          = "1995",
 volume        = "52",
 number        = "1",
 pages         = "138--140",
 issn          = "1064-5624",
 mrclass       = "47H30 (47N70 58F30 93C10)",
 mrnumber      = "1353981 (96h:47078)",
 zblnumber     = "0897.34065",
 language      = "english",
 annote        = "Consider smooth mappings
                  $f:\mathbb{R}^{d}\to\mathbb{R}^{d}$, and systems of the
                  form \[x_{n} =f(x_{n-1}).\tag{$*$}\] Equation $(*)$ usually
                  describes the dynamics of real systems only approximately,
                  and the problem arises of their roughness with respect to
                  disturbances of different natures.\par According to classic
                  results (see, e.g., [J.~Guckenheimer and P.~Holmes,
                  Nonlinear oscillations, dynamical systems, and bifurcations
                  of vector fields. Applied Mathematical Sciences, 42. New
                  York etc. Springer-Verlag (1983)]), sufficiently smooth
                  systems $(*)$ preserve many structural properties for
                  smooth disturbances (small in the metric $C^1$). To analyze
                  them, we use the technique that we proposed for an
                  approximate study of chaotic dynamical systems.\par The
                  main object of analysis is a class of operator disturbances
                  of systems $(*)$ that arises in describing the dynamics of
                  systems with weak hysteresis nonlinearities. Hysteresis
                  nonlinearities are treated in [M.~A.~Krasnosel'skij and
                  A.~V.~Pokrovskij, Systems with hysteresis. Transl. from the
                  Russian, Berlin etc.: Springer-Verlag (1989)] and in the
                  paper as continuous but fundamentally nonsmooth dynamical
                  systems $W$, often with an infinite-dimensional space
                  $\Omega=\Omega(W)$ of internal states $\omega$. This class
                  contains nonlinearities of the following types: a play, a
                  stop, Ishlinskij-Besseling's, Preisath-Giltay's, and other
                  models.",
}

@ARTICLE{DKKP:AIT95-2:e,
 author        = "Diamond, P. and Kloeden, P. and Kozyakin, V. S. and
                  Pokrovskij, A. V.",
 title         = "Robustness of the observable behavior of semihyperbolic
                  dynamic systems",
 journal       = "Autom. Remote Control",
 fjournal      = "Automation and Remote Control",
 year          = "1995",
 volume        = "56",
 number        = "11",
 pages         = "1627--1636",
 issn          = "0005-1179",
 mrclass       = "93C20 (93B07)",
 mrnumber      = "1373267 (96i:93043)",
 zblnumber     = "0931.93029",
 zblreviewer   = "Bojidar Cheshankov (Sofia)",
 language      = "english",
 annote        = "The concept of mutual shadowing formalizes the concept of
                  roughness of the observable behavior of dynamic systems and
                  can be regarded as a weak form of structural stability
                  which is useful when studying the dynamics of controlled
                  systems. The concept of mutual shadowing includes the
                  concept of shadowing of both true and pseudotrajectories of
                  a dynamic system. The systems generated by semihyperbolic
                  Lipschitz mappings, which are generally neither smooth nor
                  invertible, are shown to enjoy the mutual shadowing
                  property.",
}

@ARTICLE{DKK:JDEA08,
 author        = "Diamond, Phil and Kloeden, P. E. and Kozyakin, V. S.",
 title         = "Semi-hyperbolicity and bi-shadowing in nonautonomous
                  difference equations with {L}ipschitz mappings",
 journal       = "J. Differ. Equations Appl.",
 fjournal      = "Journal of Difference Equations and Applications",
 year          = "2008",
 volume        = "14",
 number        = "10-11",
 pages         = "1165--1173",
 issn          = "1023-6198",
 mrclass       = "37C50 (37C60 37D99 39A33)",
 mrnumber      = "2447192 (2010a:37039)",
 mrreviewer    = "Marcin Mazur",
 zblnumber     = "1154.39022",
 doi           = "10.1080/10236190802332233",
 url           = "https://www.tandfonline.com/doi/abs/10.1080/10236190802332233",
 language      = "english",
 annote        = "It is shown how known results for autonomous difference
                  equations can be adapted to definitions of
                  semi-hyperbolicity and bi-shadowing generalized to
                  nonautonomous difference equations with Lipschitz
                  continuous mappings. In particular, invertibility and
                  smoothness of the mappings are not required and, for
                  greater applicability, the mappings are allowed to act
                  between possibly different Banach spaces.",
}

@ARTICLE{DKKP:MN98,
 author        = "Diamond, Phil and Kloeden, Peter and Kozyakin, Victor and
                  Pokrovskii, Alexei",
 title         = "Boundedness and dissipativity of truncated rotations on
                  uniform planar lattices",
 journal       = "Math. Nachr.",
 fjournal      = "Mathematische Nachrichten",
 year          = "1998",
 volume        = "191",
 pages         = "59--81",
 issn          = "0025-584X",
 mrclass       = "52C05 (58F08 68U20)",
 mrnumber      = "1621361 (99f:52020)",
 mrreviewer    = "Mark J. Friedman",
 zblnumber     = "0903.65063",
 doi           = "10.1002/mana.19981910104",
 url           = "https://onlinelibrary.wiley.com/doi/abs/10.1002/mana.19981910104",
 language      = "english",
 annote        = "The finiteness of computer arithmetic can lead to some
                  dramatic differences between the behaviour of a continuous
                  dynamical system and a computer simulation. A thorough
                  rigorous theoretical analysis of what may or what does
                  happen is usually extremely difficult and to date little
                  has been done even in relatively simple contexts. The
                  comparative behaviour of a rotation mapping in the plane
                  and on a uniform lattice in the plane is one such example.
                  Simulations show that the rounding operator applied to a
                  planar rotation mapping more or less preserves the
                  qualitative behaviour of the original mapping, whereas the
                  application of the truncation operator to a planar rotation
                  can lead to quite different dynamical features. In this
                  paper a theoretical justification of the properties of the
                  planar rotation mappings under truncation to a, uniform
                  integer lattice is provided, in particular properties of
                  boundedness and dissipativity are investigated.",
}

@ARTICLE{DKKP:RCD95,
 author        = "Diamond, Phil and Kozyakin, Victor and Kloeden, Peter and
                  Pokrovskii, Alexei",
 title         = "Computer robustness of semi-hyperbolic mappings",
 journal       = "Random Comput. Dynam.",
 fjournal      = "Random {\&} Computational Dynamics",
 year          = "1995",
 volume        = "3",
 number        = "1-2",
 pages         = "57--70",
 coden         = "RCDYEM",
 issn          = "1061-835X",
 mrclass       = "58F15 (58-04 65Q05)",
 mrnumber      = "1331572 (96i:58131)",
 zblnumber     = "0849.58051",
 language      = "english",
 annote        = "Study of computer modelling of systems might necessarily
                  involve some different ideas from those used when
                  considering the underlying theoretical system acting on a
                  continuum. In this paper the idea of computer robustness of
                  a mapping f is introduced. The concept is based on the idea
                  that computer trajectories will bear some relation to what
                  is expected of the true behaviour if there is an inverse
                  shadowing property between f and its realization on a
                  computer.",
}

@BOOK{DKKP:12,
 author        = "Diamond, Phil and Kozyakin, Victor and Kloeden, Peter and
                  Pokrovskii, Alexei",
 title         = "Semi-Hyperbolicity and Bi-Shadowing",
 series        = "AIMS Series on Random and Computational Dynamics",
 publisher     = "American Institute of Mathematical Sciences",
 year          = "2012",
 volume        = "1",
 pagetotal     = "xvi+217",
 isbn          = "978-1-60133-012-3; 1-60133-012-X",
 mrclass       = "37-02 (37B20 37C50 37D05 37D20)",
 mrnumber      = "3553144",
 mrreviewer    = "Kazuhiro Sakai",
 zblnumber     = "1307.37001",
 doi           = "10.13140/RG.2.1.3119.4720",
 url           = "https://www.aimsciences.org/fileAIMS/cms/news/info/b5b22b55-5b25-4e5a-a08d-dc8214067882.pdf",
 language      = "english",
 annote        = "Semi-hyperbolicity extends the classical concept of
                  hyperbolicity for diffeomorphisms to noninvertible
                  Lipschitz mappings on sets that need not be invariant.
                  Moreover, the stable and unstable manifolds need to be
                  mapped only approximately onto their counterparts.
                  Semi-hyperbolic mappings are bi-shadowing, i.e., they also
                  satisfy a converse form of shadowing in which the
                  pseudo-orbits are not arbitrary but are the true orbits of
                  admissible classes of approximating mappings. The theory of
                  these concepts is developed systematically in this
                  monograph and illustrated through applications of nonsmooth
                  systems including those with delays and hysteresis, as well
                  as numerical approximations. Setvalued mappings are also
                  considered.",
}

@ARTICLE{KKKK:AiT83:7:e,
 author        = "Kleptsyn, A. F. and Kozyakin, V. S. and Krasnosel'skij, M.
                  A. and Kuznetsov, N. A.",
 title         = "Effect of small synchronization errors on stability of
                  complex systems. {I}",
 journal       = "Autom. Remote Control",
 fjournal      = "Automation and Remote Control",
 year          = "1983",
 volume        = "44",
 number        = "7",
 pages         = "861--867",
 issn          = "0005-1179",
 zblnumber     = "0539.93067",
 zblreviewer   = "J.Gayek",
 language      = "english",
 annote        = "A necessary and sufficient condition is given for the
                  asymptotic stability of the origin for $n$-dimensional
                  autonomous discrete linear systems with small phase lags in
                  switching. Furthermore, a sufficient condition for the
                  origin to be absolutely stable with respect to phase errors
                  is presented.",
}

@ARTICLE{KKKK:AiT84:3:e,
 author        = "Kleptsyn, A. F. and Kozyakin, V. S. and Krasnosel'skij, M.
                  A. and Kuznetsov, N. A.",
 title         = "Effect of small synchronization errors on stability of
                  complex systems. {II}",
 journal       = "Autom. Remote Control",
 fjournal      = "Automation and Remote Control",
 year          = "1984",
 volume        = "45",
 number        = "3",
 pages         = "309--314",
 issn          = "0005-1179",
 zblnumber     = "0618.93057",
 language      = "english",
 annote        = "[For part I see Autom. Remote Control 44, 861-867 (1983)].
                  Classes of linear systems with digital elements are
                  considered that are insensitive to synchronization
                  errors.",
}

@ARTICLE{KKKK:AiT84:8:e,
 author        = "Kleptsyn, A. F. and Kozyakin, V. S. and Krasnosel'skij, M.
                  A. and Kuznetsov, N. A.",
 title         = "Effect of small synchronization errors on stability of
                  complex systems. {III}",
 journal       = "Autom. Remote Control",
 fjournal      = "Automation and Remote Control",
 year          = "1984",
 volume        = "45",
 number        = "8",
 pages         = "1014--1018",
 issn          = "0005-1179",
 zblnumber     = "0604.93047",
 zblreviewer   = "J.Gayek",
 language      = "english",
 annote        = "[For the previous parts see Autom. Remote Control 45, No.3,
                  309-315 (1984) and ibid. 44, No.7, 861-867 (1983).] \par
                  Sufficiency criteria are presented for the asymptotic
                  stability of the origin for systems governed by
                  $n$-dimensional autonomous discrete-time linear equations
                  with desynchronized frequency of switching amongst the
                  state components.",
}

@ARTICLE{KKKK:DAN84:e,
 author        = "Kleptsyn, A. F. and Kozyakin, V. S. and Krasnosel'skij, M.
                  A. and Kuznetsov, N. A.",
 title         = "Stability of desynchronized systems",
 journal       = "Sov. Phys., Dokl.",
 fjournal      = "Soviet Physics. Doklady",
 year          = "1984",
 volume        = "29",
 pages         = "92--94",
 issn          = "0038-5689",
 mrclass       = "93D20",
 mrnumber      = "734942 (86e:93085)",
 zblnumber     = "0593.93046",
 zblreviewer   = "G. Leonov",
 language      = "english",
 annote        = "The concept of phase and frequency desynchronized systems is
                  introduced. These systems arise in cases when their state
                  variables are switched independently (by using independent
                  functional devices, desynchronized elements such as
                  extrapolators, memory elements etc.). For such systems
                  asymptotic stability theorems are produced.",
}

@ARTICLE{KKKK:MCS84,
 author        = "Kleptsyn, A. F. and Krasnosel'skij, M. A. and Kuznetsov, N.
                  A. and Kozjakin, V. S.",
 title         = "Desynchronization of linear systems",
 journal       = "Math. Comput. Simulation",
 fjournal      = "Mathematics and Computers in Simulation",
 year          = "1984",
 volume        = "26",
 number        = "5",
 pages         = "423--431",
 coden         = "MCSIDR",
 issn          = "0378-4754",
 mrclass       = "93D05 (93C55)",
 mrnumber      = "762920 (85j:93041)",
 zblnumber     = "0552.93051",
 zblreviewer   = "H. Fischer",
 doi           = "10.1016/0378-4754(84)90106-X",
 url           = "https://www.sciencedirect.com/science/article/pii/037847548490106X",
 language      = "english",
 annote        = "The studies of dynamics inherent in control systems which
                  incorporate sampled data elements such as extrapolators,
                  keys, memory elements, etc. are usually reduced to the
                  analysis of difference equations. However, this approach
                  tends to disregard the inevitable small desynchronization
                  of times when sampled elements are connected. In some
                  systems this desynchronization does not influence the
                  stability; otheres may be destabilized by any infinitesimal
                  desynchronization; finally, some unstable synchronized
                  systems can become asymptotically stable following the
                  introduction of any infinitesimal desynchronization. These
                  facts account for many phenomena observed in the
                  engineering practice that looked enigmatic when the
                  mathematical models ignored small desynchronization. In
                  designing the controllers the stability can be achieved by
                  introduction of lags into the system.\par The paper
                  investigates linear discrete-time (sampled-data) systems
                  with respect to stability. The systems are assumed to be
                  desynchronized in time, i.e. the time instants for sampling
                  the different state variables are incommensurable. Two
                  types of desynchronization are distinguished: a phase one
                  and a frequency one. Whereas phase-desynchronization
                  describes sampling instants $t_{i}$ to be
                  $t_{i}=nh+\tau_{i}$, frequency-desynchronization describes
                  them as $t_{i}=n(h+\delta_{i})$. Various theorems for
                  determining the stability of such systems are given without
                  proofs, which will be published in another paper. It is
                  appreciable that six examples illustrate the application of
                  the results. Here it turns out, that a system may be stable
                  if it is synchronized and may become unstable if small
                  frequency shifts are introduced: If the frequency shifts
                  become larger and larger, it is interesting to observe
                  stability for the same system again.",
}

@ARTICLE{KK:DCDSB13,
 author        = "Kloeden, P. E. and Kozyakin, V.",
 title         = "Asymptotic behaviour of random tridiagonal {M}arkov chains
                  in biological applications",
 journal       = "Discrete Contin. Dyn. Syst. Ser. B",
 fjournal      = "Discrete and Continuous Dynamical Systems. Series B. A
                  Journal Bridging Mathematics and Sciences",
 year          = "2013",
 volume        = "18",
 number        = "2",
 pages         = "453--466",
 eprinttype    = "arXiv",
 eprint        = "1112.5844",
 issn          = "1531-3492",
 mrclass       = "60J10 (15B48 92C99)",
 mrnumber      = "2999086",
 mrreviewer    = "Ross S. McVinish",
 zblnumber     = "1277.60118",
 doi           = "10.3934/dcdsb.2013.18.453",
 url           = "https://www.aimsciences.org/article/doi/10.3934/dcdsb.2013.18.453",
 language      = "english",
 annote        = "Discrete-time discrete-state random Markov chains with a
                  tridiagonal generator are shown to have a random attractor
                  consisting of singleton subsets, essentially a random path,
                  in the simplex of probability vectors. The proof uses the
                  Hilbert projection metric and the fact that the linear
                  cocycle generated by the Markov chain is a uniformly
                  contractive mapping of the positive cone into itself. The
                  proof does not involve probabilistic properties of the
                  sample path and is thus equally valid in the nonautonomous
                  deterministic context of Markov chains with, say,
                  periodically varying transitions probabilities, in which
                  case the attractor is a periodic path.",
}

@ARTICLE{KloKoz:NLINAN00,
 author        = "Kloeden, P. E. and Kozyakin, V. S.",
 title         = "The inflation of attractors and their discretization: {T}he
                  autonomous case.",
 journal       = "Nonlinear Anal.",
 fjournal      = "Nonlinear Analysis. Theory, Methods {\&} Applications.
                  Series A: Theory and Methods",
 year          = "2000",
 volume        = "40",
 number        = "1-8",
 pages         = "333--343",
 coden         = "NOANDD",
 issn          = "0362-546X",
 mrclass       = "37C50 (34D45)",
 mrnumber      = "1768417 (2002a:37031)",
 mrreviewer    = "Timothy Sauer",
 zblnumber     = "0958.37006",
 doi           = "10.1016/S0362-546X(00)85020-8",
 url           = "https://www.sciencedirect.com/science/article/pii/S0362546X00850208",
 language      = "english",
 note          = "Lakshmikantham's legacy: a tribute on his 75th birthday",
 annote        = "In this paper we introduce the concept of inflation of an
                  attractor, which will give us a larger positively invariant
                  set for the original system that contains the maximal
                  attractors of all possible autonomous perturbations and
                  discretizations of a certain size, as well as even the
                  attracting objects of corresponding nonautonomous
                  perturbations and discretizations. It also includes the
                  effects of roundoff error and converges continuously to the
                  original attractor. The existence of such an inflated
                  attractor follows from the uniform asymptotic stability of
                  the original maximal attractor. While the details and
                  underlying ideas are not really new in the autonomous case
                  considered here, the interpretation is new and is more
                  transparent here than in the technically more difficult
                  nonautonomous case, to be treated in another paper, where
                  it provides a means for handling the nonuniformities that
                  are intrinsic in nonautonomous systems.",
}

@ARTICLE{KloKoz:TRANS00,
 author        = "Kloeden, P. E. and Kozyakin, V. S.",
 title         = "The inflation of nonautonomous systems and their pullback
                  attractors",
 journal       = "Transactions of the Russian Academy of Natural Sciences,
                  Series MMMIU",
 year          = "2000",
 volume        = "4",
 number        = "1--2",
 pages         = "144--169",
 language      = "english",
 annote        = "Many original ideas and techniques that were proposed,
                  developed and applied by Mark Alexandrovich Krasnosel'skii
                  during his long career as a mathematician are being used
                  repeatedly today throughout mathematics, often without
                  knowledge or acknowledgement of their source. In this paper
                  we will see how useful several of his ideas and techniques
                  are in the context of nonautonomous dynamical systems.\par
                  The effects of perturbation or discretization of a maximal
                  attractor of autonomous dynamical systems is now well
                  understood, with the perturbed or discretized system having
                  a nearby maximal attractor. In contrast, for nonautonomous
                  systems the very concept of a nonautonomous attractor
                  itself is still undergoing intensive development and
                  perturbation or discretization results have been obtained
                  only for specific cases or under very restricted
                  assumptions.\par There are also some practical problems for
                  specific autonomous dynamical systems and types of
                  perturbation or discretization processes due to the fact
                  that the convergence of the perturbed or discretized
                  attractor to that of the original attractor is usually only
                  upper-semicontinuous convergence, which means, roughly
                  speaking, that the attractor may collapse under
                  perturbation or discretization. And what is more important,
                  this means that the internal structure of the attractor may
                  change following such a perturbation. While this is not
                  unexpected for systems with parameter values near a
                  bifurcation parameter, it does raise concerns about the
                  faithfulness of numerical approximations. Of course, this
                  collapse may not occur for another numerical scheme or step
                  size or under appropriate assumptions about the dynamics
                  inside the original attractor, but such details may not be
                  known or confirmable in practice.",
}

@ARTICLE{KloKoz:JDEA01,
 author        = "Kloeden, P. E. and Kozyakin, V. S.",
 title         = "Single parameter dissipativity and attractors in discrete
                  time asynchronous systems",
 journal       = "J. Differ. Equations Appl.",
 fjournal      = "Journal of Difference Equations and Applications",
 year          = "2001",
 volume        = "7",
 number        = "6",
 pages         = "873--894",
 coden         = "JDEAEA",
 issn          = "1023-6198",
 mrclass       = "37B25 (37B55 39A12)",
 mrnumber      = "1870728 (2002m:37020)",
 mrreviewer    = "S. Yu. Pilyugin",
 zblnumber     = "0999.93042",
 doi           = "10.1080/10236190108808309",
 url           = "https://www.tandfonline.com/doi/abs/10.1080/10236190108808309",
 language      = "english",
 note          = "On the occasion of the 60th birthday of Calvin Ahlbrandt",
 annote        = "Discrete time nonautonomous dynamical systems generated by
                  nonautonomous difference equations are formulated as
                  discrete time skew-product systems consisting of cocycle
                  state mappings that are driven by discrete time autonomous
                  dynamical systems. Forwards and pullback attractors are two
                  possible generalizations of autonomous attractors to such
                  systems. Their existence follows from appropriate forwards
                  or pullback dissipativity conditions. For discrete time
                  nonautonomous dynamical systems generated by asynchronous
                  systems with frequency updating components such a
                  dissipativity condition is usually known for a single
                  starting parameter value of the driving system. Additional
                  conditions that then ensure the existence of a forwards or
                  pullback attractor for such an asynchronous system are
                  investigated here.",
}

@ARTICLE{KloKoz:DCDS01,
 author        = "Kloeden, Peter E. and Kozyakin, Victor S.",
 title         = "The perturbation of attractors of skew-product flows with a
                  shadowing driving system",
 journal       = "Discrete Contin. Dyn. Syst.",
 fjournal      = "Discrete and Continuous Dynamical Systems",
 year          = "2001",
 volume        = "7",
 number        = "4",
 pages         = "883--893",
 issn          = "1078-0947",
 mrclass       = "37C70 (34D45 37C10 37C50)",
 mrnumber      = "1849667 (2002d:37042)",
 mrreviewer    = "Kazuhiro Sakai",
 zblnumber     = "1013.37021",
 doi           = "10.3934/dcds.2001.7.883",
 language      = "english",
 annote        = "The influence of the driving system on a skew-product flow
                  generated by a triangular system of differential equations
                  can be perturbed in two ways, directly by perturbing the
                  vector field of the driving system component itself or
                  indirectly by perturbing its input variable in the vector
                  field of the coupled component. The effect of such
                  perturbations on a nonautonomous attractor of the driven
                  component is investigated here. In particular, it is shown
                  that a perturbed nonautonomous attractor with nearby
                  components exists in the indirect case if the driven system
                  has an inflated nonautonomous attractor and that the direct
                  case can be reduced to this case if the driving system is
                  shadowing.",
}

@ARTICLE{KloKoz:DCDSA04,
 author        = "Kloeden, Peter E. and Kozyakin, Victor S.",
 title         = "Uniform nonautonomous attractors under discretization",
 journal       = "Discrete Contin. Dyn. Syst.",
 fjournal      = "Discrete and Continuous Dynamical Systems. Series A",
 year          = "2004",
 volume        = "10",
 number        = "1-2",
 pages         = "423--433",
 issn          = "1078-0947",
 mrclass       = "37C60 (34D10 34D45 37B25 37C70)",
 mrnumber      = "2026203 (2004m:37038)",
 mrreviewer    = "Igor D. Chueshov",
 zblnumber     = "1047.37015",
 doi           = "10.3934/dcds.2004.10.423",
 url           = "https://www.aimsciences.org/article/doi/10.3934/dcds.2004.10.423",
 language      = "english",
 annote        = "A nonautonomous or cocycle dynamical system that is driven
                  by an autonomous dynamical system acting on a compact
                  metric space is assumed to have a uniform pullback
                  attractor. It is shown that discretization by a one-step
                  numerical scheme gives rise to a discrete time cocycle
                  dynamical system with a uniform pullback attractor, the
                  component subsets of which converge upper semi continuously
                  to their continuous time counterparts as the maximum time
                  step decreases to zero. The proof involves a Lyapunov
                  function characterizing the uniform pullback attractor of
                  the original system.",
}

@ARTICLE{KloKoz:MESA11,
 author        = "Kloeden, Peter E. and Kozyakin, Victor S.",
 title         = "The dynamics of epidemiological systems with nonautonomous
                  and random coefficients",
 journal       = "Mathematics in Engineering, Science and Aerospace",
 year          = "2011",
 volume        = "2",
 number        = "2",
 pages         = "105--118",
 zblnumber     = "1215.37016",
 url           = "http://nonlinearstudies.com/index.php/mesa/article/view/652",
 language      = "english",
 annote        = "Steady state solutions are important in characterizing the
                  asymptotic behaviour of epidemiological systems such as the
                  ubiquitous SIR system, but they need not exist when the
                  coefficients vary with time. Recent developments in the
                  theory of nonautonomous dynamical systems provide the
                  appropriate counterpart, time varying nonautonomous
                  equilibria, i.e., entire solutions determined by pullback
                  attraction. These will be illustrated here through explicit
                  solutions for the simpler SI system. For the more
                  complicated SIR system it will be shown how pullback
                  attractors provide additional insight into dynamics,
                  especially the chaotic dynamics induced by periodical
                  forcing.",
}

@ARTICLE{KK:BAMS13,
 author        = "Kloeden, Peter E. and Kozyakin, Victor S.",
 title         = "Asymptotic behaviour of random {M}arkov chains with
                  tridiagonal generators",
 journal       = "Bull. Aust. Math. Soc.",
 fjournal      = "Bulletin of the Australian Mathematical Society",
 year          = "2013",
 volume        = "87",
 number        = "1",
 pages         = "27--36",
 month         = feb,
 eprinttype    = "arXiv",
 eprint        = "1201.1999",
 issn          = "0004-9727",
 mrclass       = "60J27 (34F05 37H10 60H25)",
 mrnumber      = "3011939",
 mrreviewer    = "Wenqing Hu",
 zblnumber     = "1268.34105",
 doi           = "10.1017/S0004972712000160",
 language      = "english",
 annote        = "Continuous-time discrete-state random Markov chains
                  generated by a random linear differential equation with a
                  random tridiagonal matrix are shown to have a random
                  attractor consisting of singleton subsets, essentially a
                  random path, in the simplex of probability vectors. The
                  proof uses comparison theorems for Caratheodory random
                  differential equations and the fact that the linear cocycle
                  generated by the Markov chain is a uniformly contractive
                  mapping of the positive cone into itself with respect to
                  the Hilbert projective metric. It does not involve
                  probabilistic properties of the sample path and is thus
                  equally valid in the nonautonomous deterministic context of
                  Markov chains with, say, periodically varying transition
                  probabilities, in which case the attractor is a periodic
                  path.",
}

@INPROCEEDINGS{KloKoz:ICDE04,
 author        = "Kloeden, Peter and Kozyakin, Victor",
 editor        = "Aulbach, Bernd and Elaydi, Saber and Ladas, Gerasimos",
 title         = "The inflation and perturbation of nonautonomous difference
                  equations and their pullback attractors",
 booktitle     = "Proceedings of the {S}ixth {I}nternational {C}onference on
                  {D}ifference {E}quations",
 publisher     = "CRC",
 address       = "Boca Raton, FL",
 year          = "2004",
 pages         = "139--152",
 mrclass       = "34D45 (37B55 37C70)",
 mrnumber      = "2092551 (2005f:34146)",
 mrreviewer    = "Ioannis K. Purnaras",
 zblnumber     = "1062.37009",
 language      = "english",
 annote        = "Nonautonomous difference equations are formulated as
                  difference cocycles driven by an autonomous dynamical
                  system. Pullback attractors are the appropriate
                  generalization of autonomous attractors to cocycles and
                  their existence follows when the difference cocycle has a
                  pullback absorbing set. The effects of perturbing the
                  driving autonomous system of a difference cocycle are
                  considered here, in the weaker sense of perturbations of
                  its input variable in the nonautonomous difference equation
                  and in the stronger sense of the driving system being
                  perturbed to a nearby driving system. The existence of a
                  pullback attractor of the in ated cocycle dynamics and the
                  shadowing of the driving system are important assumptions
                  here.",
}

@ARTICLE{Koz:TrVGU72:e,
 author        = "Kozjakin, V. S.",
 title         = "The inverse {M}inkowski inequality for monotone functions",
 journal       = "Vorone{\v{z}}. Gos. Univ. Trudy Naucn.-Issled. Inst. Mat.
                  VGU",
 year          = "1972",
 number        = "Vyp. 5 Sb. Statei Teor. Operator. i Differencial.
                  Uravnenii",
 pages         = "59--64",
 mrclass       = "26A86",
 mrnumber      = "0442175 (56 \#561)",
 language      = "english",
 note          = "In Russian",
}

@ARTICLE{Koz:UMN72:e,
 author        = "Kozjakin, V. S.",
 title         = "The vibrostability of second order differential equations",
 journal       = "Uspehi Mat. Nauk",
 fjournal      = "Akademiya Nauk SSSR i Moskovskoe Matematicheskoe
                  Obshchestvo. Uspekhi Matematicheskikh Nauk",
 year          = "1972",
 volume        = "27",
 number        = "5(167)",
 pages         = "241--242",
 issn          = "0042-1316",
 mrclass       = "34D99",
 mrnumber      = "0393705 (52 \#14514)",
 mrreviewer    = "M. M. Konstantinov",
 zblnumber     = "0245.93023",
 language      = "english",
 note          = "In Russian",
}

@INCOLLECTION{Koz:DE76-1:e,
 author        = "Kozjakin, V. S.",
 title         = "A second necessary condition for the bifurcation of
                  {$N$}-periodic points",
 booktitle     = "Differential equations ({R}ussian)",
 publisher     = "Ku{\u\i}by{\v{s}}ev. Gos. Univ., Kuybyshev",
 year          = "1976",
 pages         = "39--44, 167",
 mrclass       = "58F10 (58E05)",
 mrnumber      = "0516349 (58 \#24362)",
 language      = "english",
 note          = "In Russian",
}

@INCOLLECTION{Koz:DE76-2:e,
 author        = "Kozjakin, V. S.",
 title         = "The break-up of invariant tori",
 booktitle     = "Differential equations ({R}ussian)",
 publisher     = "Ku{\u\i}by{\v{s}}ev. Gos. Univ., Kuybyshev",
 year          = "1976",
 pages         = "45--50, 167",
 mrclass       = "58F10 (34C15 34D30)",
 mrnumber      = "0516351 (58 \#24363)",
 language      = "english",
 note          = "In Russian",
}

@ARTICLE{Koz:DAN77:232:e,
 author        = "Kozjakin, V. S.",
 title         = "Subfurcation of periodic oscillations",
 journal       = "Sov. Math., Dokl.",
 fjournal      = "Soviet Mathematics. Doklady",
 year          = "1977",
 volume        = "18",
 pages         = "18--21",
 issn          = "0197-6788",
 mrclass       = "34C15 (58F20 92A05)",
 mrnumber      = "0430421 (55 \#3426)",
 mrreviewer    = "A. A. Reinfelds",
 zblnumber     = "0371.34023",
 language      = "english",
 annote        = "A number $\lambda_{0}$ is called a subfurcation point in the
                  problem of subharmonic oscillations if for certain
                  $\lambda_{k}\to\lambda_{0}$ the system $dx/dt =
                  f(t,x,\lambda)$, with a right-hand side that is
                  $T$-periodic in $t$ and that depends on a scalar parameter
                  $\lambda$, has periodic solutions $x_{k}(t)$ whose
                  amplitudes tend to zero and whose least periods $T_{k}$
                  increase unboundedly. In this paper the author supposes
                  that $f(t,0,\lambda)\equiv 0$ and elucidates the conditions
                  under which a number $\lambda_{0}$ has to be a subfurcation
                  point.",
}

@ARTICLE{Koz:UMN77:e,
 author        = "Kozjakin, V. S.",
 title         = "The generation of periodic points from an equilibrium
                  position",
 journal       = "Uspehi Mat. Nauk",
 fjournal      = "Akademiya Nauk SSSR i Moskovskoe Matematicheskoe
                  Obshchestvo. Uspekhi Matematicheskikh Nauk",
 year          = "1977",
 volume        = "32",
 number        = "4 (196)",
 pages         = "255--256",
 issn          = "0042-1316",
 mrclass       = "58F20",
 mrnumber      = "0467843 (57 \#7694)",
 mrreviewer    = "Milan Medved'",
 zblnumber     = "0362.34029",
 language      = "english",
 note          = "In Russian",
}

@INPROCEEDINGS{Koz:CDC05:e,
 author        = "Kozyakin, V.",
 title         = "A Dynamical Systems Construction of a Counterexample to the
                  Finiteness Conjecture",
 booktitle     = "Proceedings of the 44th IEEE Conference on Decision and
                  Control, 2005 and 2005 European Control Conference.
                  CDC-ECC'05.",
 year          = "2005",
 pages         = "2338--2343",
 doi           = "10.1109/CDC.2005.1582511",
 url           = "https://ieeexplore.ieee.org/document/1582511",
 language      = "english",
 annote        = "In 1995 J.~C.~Lagarias and Y.~Wang conjectured that the
                  generalized spectral radius of a finite set of matrices can
                  be attained on a finite product of matrices. The first
                  counterexample to this Finiteness Conjecture was given in
                  2002 by T.~Bousch and J.~Mairesse. In 2003 V.~D.~Blondel,
                  J.~Theys and A.~A.~Vladimirov proposed another proof of a
                  counterexample to the Finiteness Conjecture which
                  extensively exploited combinatorial properties of matrix
                  products. In the paper, it is proposed one more proof of a
                  counterexample of the Finiteness Conjecture fulfilled in a
                  traditional manner of the theory of dynamical systems. It
                  is presented description of the structure of trajectories
                  with the maximal growing rate in terms of extremal norms
                  and associated with them so-called extremal trajectories.
                  The construction of the counterexample is based on a
                  detailed analysis of properties of extremal norms of
                  two-dimensional positive matrices in which the technique of
                  the Gram symbols is essentially used. At last, notions and
                  properties of the rotation number for discontinuous
                  orientation preserving circle maps play significant role in
                  the proof.",
}

@ARTICLE{KKPV:NATMA97,
 author        = "Kozyakin, V. and Kuznetsov, N. and Pokrovskii, A. and
                  Vladimirov, I.",
 title         = "Some problems in analysis of discretizations of continuous
                  dynamical systems",
 journal       = "Nonlinear Anal.",
 fjournal      = "Nonlinear Analysis. Theory, Methods {\&} Applications. An
                  International Multidisciplinary Journal. Series A: Theory
                  and Methods",
 year          = "1997",
 volume        = "30",
 number        = "2",
 pages         = "767--778",
 coden         = "NOANDD",
 issn          = "0362-546X",
 mrclass       = "58F08 (65D99)",
 mrnumber      = "1487659 (98j:58065)",
 mrreviewer    = "Peter E. Kloeden",
 zblnumber     = "0888.39011",
 doi           = "10.1016/S0362-546X(96)00232-5",
 url           = "https://www.sciencedirect.com/science/article/pii/S0362546X96002325",
 language      = "english",
 note          = "Proceedings of the {S}econd {W}orld {C}ongress of
                  {N}onlinear {A}nalysts, {P}art 2 ({A}thens, 1996)",
 annote        = "The traditional approach to numerical methods is based on
                  the fundamental hypothesis that any required accuracy of
                  solution of a problem can be achieved by means of
                  appropriate precision of computer arithmetic, extending
                  computer memory and time of calculation. This hypothesis is
                  strongly supported by many rigorous theoretical methods of
                  mathematics and theoretical physics and many heuristic and
                  empirical tools. Nevertheless, recently computer modeling
                  is often applied just for the analysis of those problems
                  where the reliable theoretical methods of understanding the
                  relationships between properties of the continuous objects
                  and their discretized counterparts are not applicable and,
                  at the same time, empirically justified tools are not yet
                  adequate. The paper is dedicated mainly to analysis of two
                  examples of such situation. The first example concerns the
                  discrepances between behavior of some continuous
                  one-dimensional chaotic systems and their discretized
                  counterparts. The second example deals with discrepances
                  between phase diagram of rotation of the plane with some
                  fixed angle and natural discretizations of this mappings.",
}

@ARTICLE{Koz:MATZAME72:e,
 author        = "Kozyakin, V. S.",
 title         = "A functional equation",
 journal       = "Math. Notes",
 fjournal      = "Mathematical notes of the Academy of Sciences of the USSR",
 year          = "1971",
 volume        = "9",
 number        = "2",
 pages         = "95--100",
 issn          = "0001-4346",
 mrclass       = "39.38",
 mrnumber      = "0277944 (43 \#3677)",
 zblnumber     = "0222.47006",
 doi           = "10.1007/BF01316987",
 language      = "english",
 annote        = "Existence theorems for and the determination of continuous
                  solutions, defined on the real axis $R$, of the functional
                  equation $f(t)=A[t,f(at-b),f(at-c)]$, where $a, b$, and $c$
                  are real parameters, $A:R\times E\times E \to E$ is a
                  continuous operator, and $E$ is a Banach space.",
}

@ARTICLE{Koz:SMZh77:e,
 author        = "Kozyakin, V. S.",
 title         = "Subfurcation in loss of stability of equilibrium position
                  for a system of differential equations with lag",
 journal       = "Sib. Math. J.",
 fjournal      = "Siberian Mathematical Journal",
 year          = "1977",
 volume        = "18",
 number        = "3",
 pages         = "414--425",
 issn          = "0037-4466",
 mrclass       = "34K20",
 mrnumber      = "0481372",
 mrreviewer    = "Russell C. Thompson",
 zblnumber     = "0414.34079",
 doi           = "10.1007/BF00967033",
 url           = "https://link.springer.com/article/10.1007/BF00967033",
 language      = "english",
 annote        = "We consider a system of differential equations with lagging
                  argument and dependent on a scalar parameter $\lambda$,
                  viz., \[ \frac{dx}{dt}=f(\lambda,t,x_{t}). \] Here $x=
                  \{x_{1}, x_{2},\ldots,x_{n}\}$ is a point in the space
                  $R^{n}$; the symbol $x_{t}$ denotes the continuous vector
                  function
                  $x_{t}(s)=\{x_{1}(t+s),x_{2}(t+s),\ldots,x_{n}(t+s)\}$ in
                  the variable $s\in [-h, 0]$ $(h\ge 0)$;
                  $f(\lambda,t,x_{t})$ is an operator $T$-periodic in $t$
                  $(T>0)$ with values in $R^{n}$ and defined for the third
                  argument on the set of functions continuous on $[-h, 0]$ of
                  sufficiently small uniform norm, and
                  $f(\lambda,t,0)\equiv0$.\par We can represent in such a
                  form, e.g., a system of differential equations with several
                  discrete lags or a system with several distributed lags and
                  likewise many differential equations with more complicated
                  types of lagging argument.\par Suppose the zero solution of
                  the system under consideration is stable for
                  $\lambda=\lambda_{1}$, but unstable for
                  $\lambda=\lambda_{2}$ $(\lambda_{1}<\lambda_{2})$. Then
                  there is a point $\lambda=\lambda_{0}$ \emph{of stability
                  loss} of the zero solution of the system which
                  characterized by the fact that for
                  $\lambda_{1}\le\lambda<\lambda_{0}$ the zero solution is
                  stable but arbitrarily close to the right of $\lambda_{0}$
                  are values of the parameter for which the zero solution is
                  unstable.\par In a number of problems it is important to
                  know how stability loss occurs for the zero solution of a
                  system. This is one of the classical problems in the theory
                  of stability of motion. Solutions of this problem in
                  various situations have been the concern of an extensive
                  literature. In the work, we study a new situation of a
                  general form. We call $\lambda_{0}$ \emph{a subfurcation
                  point} of periodic solutions if the system has for certain
                  $\lambda_{k}\to\lambda_{0}$ nonzero periodic solutions
                  whose amplitudes tend to zero as $k\to\infty$ and whose
                  smallest periods grow without bound. We show that for a
                  rather broad class of $f(\lambda,t,x_{t})$ stability loss
                  of the zero solution is accompanied ``almost always'' by
                  subfurcation. This result is new even for equations without
                  lag.",
}

@ARTICLE{Koz:AiT84:10:e,
 author        = "Kozyakin, V. S.",
 title         = "Neglecting small terms in the study of nonlinear systems",
 journal       = "Autom. Remote Control",
 fjournal      = "Automation and Remote Control",
 year          = "1984",
 volume        = "45",
 pages         = "1275--1280",
 issn          = "0005-1179",
 mrclass       = "93C10",
 mrnumber      = "794181 (86g:93042)",
 mrreviewer    = "Vadim Komkov",
 zblnumber     = "0571.93029",
 language      = "english",
 annote        = "Tests are proposed which allow one to judge when neglecting
                  terms of higher order of smallness is admissible in
                  problems of the analysis of nonlinear systems.",
}

@ARTICLE{Koz:AiT85:9:e,
 author        = "Kozyakin, V. S.",
 title         = "Observability of periodic modes that arise in the loss of
                  stability of the equilibrium state of sampled-data
                  systems",
 journal       = "Autom. Remote Control",
 fjournal      = "Automation and Remote Control",
 year          = "1985",
 volume        = "46",
 pages         = "1098--1104",
 issn          = "0005-1179",
 mrclass       = "93C57 (58F14)",
 mrnumber      = "809662 (86j:93021)",
 zblnumber     = "0597.93009",
 zblreviewer   = "A. Van{\v{e}}{\v{c}}ek",
 language      = "english",
 annote        = "A nonlinear sampled-data control system with $n$-dimensional
                  state $x$ and scalar parameter $\lambda$ is considered:
                  $x(n+1)=f(x(n),\lambda)$. The degree of observability of
                  periodic modes is introduced by the rate of occurrence of
                  the values of $\lambda$ in the sequence
                  $\lambda_1,\lambda_2,\ldots$. for which the system has
                  asymptotically stable periodic modes, and the properties of
                  such observability are studied.",
}

@INCOLLECTION{KozMTS:86:e,
 author        = "Kozyakin, V. S.",
 editor        = "Krasnosel'ski{\u\i}, M. A.",
 title         = "Criteria of finite determinedness",
 booktitle     = "Matematicheskaya teoriya sistem",
 chapter       = "8",
 publisher     = "Nauka",
 address       = "Moscow",
 year          = "1986",
 pages         = "136--160",
 language      = "english",
 note          = "In Russian",
 annote        = "The analysis of the problems of the mathematical theory of
                  systems is connected with the study of the structure of the
                  solution set of nonlinear equations. As a rule, non-linear
                  equations are complex for research and they have to be
                  ``simplified'' in some way. In some cases this leads to
                  correct conclusions about the structure of the set of
                  solutions of the original equations, in others to false
                  ones. Often, small solutions of the equations are of
                  interest. In this case, a common way to simplify the
                  equations is to truncate them; that is to discard in the
                  power expansions of the left-hand sides the terms of high
                  degrees. The transition to truncated equations is analogous
                  to the analysis of stability by the first approximation,
                  analysis of bifurcations in nonlinear problems by
                  transition to linearized equations, etc. In this chapter we
                  study the admissibility of truncation in the study of
                  systems of real nonlinear equations.",
}

@ARTICLE{Koz:DAN90:312:e,
 author        = "Kozyakin, V. S.",
 title         = "Absolute stability of discrete desynchronized systems",
 journal       = "Sov. Phys., Dokl.",
 fjournal      = "Soviet Physics. Doklady",
 year          = "1990",
 volume        = "35",
 number        = "6",
 pages         = "518--519",
 issn          = "0038-5689",
 mrclass       = "93D05 (93C55)",
 mrnumber      = "1070889 (91m:93083)",
 zblnumber     = "0734.93048",
 zblreviewer   = "Cui Baotong (Binzhou)",
 language      = "english",
 annote        = "Let $\mathfrak{F}$ be a family of mappings: $F:R^N\to R^N $,
                  $F(0)=0$. The function $x(\cdot)$ is said to belong to the
                  set $\mathfrak{M}_{k}(\mathfrak{F})$ (or
                  $\mathfrak{M}_{-\infty}(\mathfrak{F})$), if there exist
                  $F(n,\cdot)\in\mathfrak{F}$, such that for $n\ge k$ (or for
                  all integer $n$) \[x(n+1)=F(n,x(n)).\tag{$*$}\] The author
                  considers the absolute stability of $(*)$ and some results
                  are obtained.",
}

@ARTICLE{Koz:AiT90:10:e,
 author        = "Kozyakin, V. S.",
 title         = "Absolute stability of systems with asynchronous sampled-data
                  elements",
 journal       = "Autom. Remote Control",
 fjournal      = "Automation and Remote Control",
 year          = "1990",
 volume        = "51",
 number        = "10",
 pages         = "1349--1355",
 issn          = "0005-1179",
 mrclass       = "93D05 (93C57)",
 mrnumber      = "1088520 (91j:93070)",
 zblnumber     = "0737.93055",
 zblreviewer   = "E. Yaz (Fayetteville)",
 language      = "english",
 annote        = "The author considers the problem of asynchronous operation
                  of elements in sampled-data systems. The concepts of
                  absolute neutral and asymptotic stability with respect to
                  different asynchronous operation classes are introduced and
                  results characterizing such properties of asynchronous
                  systems are presented.",
}

@ARTICLE{Koz:AiT90:6:e,
 author        = "Kozyakin, V. S.",
 title         = "Algebraic unsolvability of problem of absolute stability of
                  desynchronized systems",
 journal       = "Autom. Remote Control",
 fjournal      = "Automation and Remote Control",
 year          = "1990",
 volume        = "51",
 number        = "6",
 pages         = "754--759",
 issn          = "0005-1179",
 mrclass       = "93D09 (93C55)",
 mrnumber      = "1071607 (91e:93065)",
 zblnumber     = "0737.93056",
 language      = "english",
 annote        = "In complex control systems containing sampled-data elements,
                  it is possible that these elements operate asynchronously.
                  In some cases asynchronous character of operation of
                  sampled-data elements does not influence stability of
                  system. In other cases any small desynchronization of the
                  updating moments of sampled-data elements leads to dramatic
                  changes of dynamics of a control system, and the system
                  loses stability. Last years there is begun intensive
                  studying of the effects connected with asynchronous
                  operation of control systems; both necessary, and
                  sufficient stability conditions for various classes of
                  asynchronous systems were obtained. At the same time no one
                  succeed in finding general, effectively verified criteria
                  of stability of asynchronous systems, similar to known for
                  synchronous systems. The problem on stability of linear
                  asynchronous systems has appeared more difficult than the
                  problem on stability of synchronous systems. In the paper,
                  attempt of formal explanation of complexity of the
                  stability analysis problem for linear asynchronous systems
                  is undertaken. It is shown that there are no criteria of
                  absolute stability of linear asynchronous systems
                  consisting of a finite number of arithmetic operations.",
}

@ARTICLE{Koz:DAN90:311:e,
 author        = "Kozyakin, V. S.",
 title         = "Stability analysis of asynchronous systems by methods of
                  symbolic dynamics",
 journal       = "Sov. Phys., Dokl.",
 fjournal      = "Soviet Physics. Doklady",
 year          = "1990",
 volume        = "35",
 number        = "3",
 pages         = "218--220",
 issn          = "0038-5689",
 mrclass       = "93C57 (54H20)",
 mrnumber      = "1075682 (92c:93056)",
 mrreviewer    = "Nikita E. Barabanov",
 zblnumber     = "0713.93045",
 language      = "english",
 annote        = "The dynamics of autonomous control systems with sampled-data
                  elements is described, by the equations
                  \[x_i(T^{ij}+0)=f_i[x_1(T^{ij}-0),\ldots,x_k(T^{ij}-0)],\quad
                  i=1,\ldots,k,\] where each vector function $x_i(t)$ with
                  values in $R_{n_i}$ is constant on the intervals
                  $T^{ij}<t<T^{ij+1}$. In the classical theory of
                  sampled-data systems, the switching times $T^{ij}$ are the
                  same for all components $x_i$, i.e.,
                  $T^{1j}=T^{2j}=\ldots=T^{kj}$. A rich arsenal of methods
                  for the analysis of the dynamics of the systems under
                  consideration has been developed for this case.\par An
                  important class are phase-frequency asynchronous systems
                  (1) with switching times $T^{ij}=\phi_i+j^{\omega_i}$.
                  \emph{A.~F.~Kleptsyn} [Avtom. Telemekh. 1985, No.4, 169-171
                  (1985)] and \emph{A.~F.~Kleptsyn},
                  \emph{M.~A.~Krasnosel'skij}, \emph{N.~A.~Kuznetsov} and the
                  author [Math. Comput. Simulation 26, 423-431 (1984)] noted
                  that the stability of these systems is closely linked with
                  the properties of sequences of symbols called shift texts.
                  This observation has led to important theorems on stability
                  of linear two-component phase-frequency asynchronous
                  control systems.",
}

@ARTICLE{Koz:AiT90:8:e,
 author        = "Kozyakin, V. S.",
 title         = "Stability of phase-frequency desynchronized systems under a
                  perturbation of the switching instants of the components",
 journal       = "Autom. Remote Control",
 fjournal      = "Automation and Remote Control",
 year          = "1990",
 volume        = "51",
 number        = "8",
 pages         = "1034--1040",
 issn          = "0005-1179",
 mrclass       = "93D09",
 mrnumber      = "1080599 (91j:93078)",
 zblnumber     = "0735.93067",
 zblreviewer   = "D. Franke (Hamburg)",
 language      = "english",
 annote        = "The paper studies a control problem for systems with
                  discrete elements which has found little attention in the
                  past. Two distance subsystems are assumed to exchange
                  information periodically. This is done non-synchronously,
                  because sach subsystem is assumed to have its individual
                  periodicity. Asymptotic stability of the zero equilibrium
                  position of the overall system is investigated in presence
                  of small perturbations of the periods and the phases of
                  switching of the subsystems.",
}

@ARTICLE{Koz:IFACPV,
 author        = "Kozyakin, V. S.",
 title         = "Equivalent norms technique for stability analysis of linear
                  discrete event systems",
 journal       = "IFAC Proceedings Volumes",
 year          = "1991",
 volume        = "24",
 number        = "14",
 pages         = "290--295",
 keywords      = "desynchronized systems; linear systems; stability problem;
                  equivalent norms technique; robustness",
 issn          = "1474-6670",
 doi           = "10.1016/S1474-6670(17)69372-8",
 url           = "https://www.sciencedirect.com/science/article/pii/S1474667017693728",
 language      = "english",
 note          = "IFAC Workshop on Discrete Event System Theory and
                  Applications in Manufacturing and Social Phenomena,
                  Shenyang, China, June 25-27, 1991",
 annote        = "Linear desynchronized systems are considered that are
                  particular (but very important) case of the so-called
                  Discrete Event Dynamic Systems. The stability problem of
                  linear desynchronized systems is studied for the most
                  unfavorable situation --- when neither information
                  concerning rules of alteration of updating moments for
                  different subsystems nor information concerning the amount
                  of subsystems updating at any time instant is available.
                  The Equivalent Norms Technique for stability analysis of
                  desynchronized systems is presented. Obstacles for
                  application of this technique are discussed and the way to
                  overcome them is shown. To demonstrate the potential of the
                  Equivalent Norms Technique some examples are presented.
                  Among them the proof of robustness of linear desynchronized
                  systems with regard to deviations of parameters inherent in
                  a system. With the help of the Equivalent Norms Technique
                  it is proved also that asymptotically stable linear
                  desynchronized systems are stable under constantly acting
                  perturbations. One new class of stable linear
                  desynchronized systems is described.",
}

@ARTICLE{Koz:DAN91:e,
 author        = "Kozyakin, V. S.",
 title         = "Perturbation of linear asynchronous systems",
 journal       = "Sov. Phys., Dokl.",
 fjournal      = "Soviet Physics. Doklady",
 year          = "1991",
 volume        = "36",
 number        = "1",
 pages         = "16--17",
 issn          = "0038-5689",
 mrclass       = "93D09",
 mrnumber      = "1102773",
 zblnumber     = "0752.93064",
 zblreviewer   = "L. Rodman (Williamsburg)",
 language      = "english",
 annote        = "A system $W$ is described by its state space
                  $X=\{x=(x_1,x_2,\ldots,x_N)^T: x_i\in\mathbb{R}^{n_i}\}$
                  and dynamics $x(0)=0$, $x(n+1)=A_{w(n)}x(n)+F(n)$, $F(n)\in
                  X_{w(n)}$, $n=0,1,\ldots$, where $w=\{w(n)\}^\infty_{n=1}$
                  is a sequence of subsets $w(n)\subseteq\{1,\ldots,N\}$.
                  Here $A=[a_{ij}]^N_{i,j=1}$ is a fixed block matrix,
                  $A_{w(n)}$ is obtained from $A$ by replacing its block rows
                  corresponding to indices $i\not\in w(n)$ with the
                  corresponding rows of the identity matrix, and
                  \[X_{w(n)}=\{(x_1,\ldots,x_n)^T\in X:\quad
                  x_i=0\quad\text{if}\quad i\not\in w(n)\}.\] The system $W$
                  with the matrix $A$ is called Perron absolutely stable if
                  there is $\beta<\infty$ such that for any sequence $w$ of
                  subsets in $\{1,\ldots,N\}$ and any choice of $F(n)\in
                  X_{w(n)}$ satisfying $\|F(n)\|\le 1$, the state $x(n)$
                  satisfies the inequality $\|x(n)\|\le\beta$ for all $n$.
                  Perron absolutely stability is characterized in terms of
                  existence of a norm in $X$ with special properties.",
}

@ARTICLE{Koz:AiT91:e,
 author        = "Kozyakin, V. S.",
 title         = "Stability of linear desynchronized systems with unsymmetric
                  matrices",
 journal       = "Autom. Remote Control",
 fjournal      = "Automation and Remote Control",
 year          = "1991",
 volume        = "52",
 number        = "7",
 pages         = "928--933",
 issn          = "0005-1179",
 mrclass       = "93D09",
 mrnumber      = "1139401 (92h:93064)",
 zblnumber     = "0744.93083",
 language      = "english",
 annote        = "A new criterion of asymptotic stability is established for
                  linear desynchronized systems. We show that the problem of
                  preserving absolute asymptotic stability in the presence of
                  small matrix perturbation in linear desynchronized systems
                  is equivalent to the problem of stability in the presence
                  of persistent perturbations.",
}

@TECHREPORT{Koz:BCRI03-13,
 author        = "Kozyakin, V. S.",
 title         = "Asynchronous Systems: A Short Survey and Problems",
 institution   = "Boole Centre for Research in Informatics, University College
                  Cork --- National University of Ireland",
 address       = "Cork",
 year          = "2003",
 number        = "13/2003",
 pagetotal     = "19",
 type          = "Preprint",
 month         = may,
 url           = "https://www.researchgate.net/publication/228863199",
 language      = "english",
 annote        = "Looking at the dynamics of the system described by the
                  equation $x(n + 1) = f(x(n))$ one may say that coordinates
                  of the vector $x = {x_{1}, x_{2}, \ldots , x_{N}}$ are
                  updated synchronously. What happens with the system if
                  coordinates of the vector $x$ are updated asynchronously,
                  i.e., if at a given moment $n$ only coordinates with
                  indices $i$ from some set $w(n) \subseteq {1,2,\ldots,N}$
                  are changed in accordance with the law $x_{i}(n+1) =
                  f_{i}(x(n))$ while others remain intact? This is the main
                  topic which is discussed in the paper.",
}

@TECHREPORT{Koz:BCRI03-12,
 author        = "Kozyakin, V. S.",
 title         = "Discontinuous Order Preserving Circle Maps Versus Circle
                  Homeomorphisms",
 institution   = "Boole Centre for Research in Informatics, University College
                  Cork --- National University of Ireland",
 address       = "Cork",
 year          = "2003",
 number        = "12/2003",
 pagetotal     = "17",
 type          = "Preprint",
 month         = may,
 url           = "https://www.researchgate.net/publication/234109557",
 language      = "english",
 annote        = "The theory of circle homeomorphisms has a great number of
                  deep results. However, sometimes continuity of a circle map
                  may be restrictive in theoretical constructions or
                  applications. In this paper it is shown that some principal
                  properties of circle homeomorphisms are inherited by the
                  class of order preserving circle maps. The latter class is
                  rather broad and contains not only circle homeomorphisms
                  but also a variety of non continuous maps arising in
                  applications. Of course, even in cases when a property
                  remains to be valid for order preserving circle maps,
                  absence of continuity sometimes results in noticeable
                  changes of related proofs.",
}

@ARTICLE{Koz:AiT03:9:e,
 author        = "Kozyakin, V. S.",
 title         = "Indefinability in o-minimal structures of finite sets of
                  matrices whose infinite products converge and are bounded
                  or unbounded",
 journal       = "Autom. Remote Control",
 fjournal      = "Automation and Remote Control",
 year          = "2003",
 volume        = "64",
 number        = "9",
 pages         = "1386--1400",
 issn          = "0005-1179",
 mrclass       = "03C64 (14P10 93B27)",
 mrnumber      = "2090805 (2005h:03070)",
 mrreviewer    = "S. R. Kogalovski{\u\i}",
 zblnumber     = "1078.93017",
 doi           = "10.1023/A:1026091717271",
 url           = "https://link.springer.com/article/10.1023/A/:1026091717271",
 language      = "english",
 annote        = "This paper is concerned with the convergence and boundedness
                  or unboundedness of the set of all possible matrix products
                  with coefficients belonging to some finite set, i.e., the
                  problem to which many problems of control theory and
                  mathematics are reduced. The indefinability of this problem
                  in o-minimal structures containing semialgebraic sets,
                  which can be regarded as a characteristic for the
                  complexity of the problem, is demonstrated. The result
                  shows, in particular, that the solution of our problem
                  cannot be found as a finite Boolean combination of
                  conditions containing a finite number of ordinary
                  arithmetical operations of addition, subtraction, and
                  multiplication, as well as exponentiation and application
                  of bounded analytic functions.",
}

@TECHREPORT{Koz:BCRI03-11,
 author        = "Kozyakin, V. S.",
 title         = "Sturmian Sequences Generated by Order Preserving Circle
                  Maps",
 institution   = "Boole Centre for Research in Informatics, University College
                  Cork --- National University of Ireland",
 address       = "Cork",
 year          = "2003",
 number        = "11/2003",
 pagetotal     = "16",
 type          = "Preprint",
 month         = may,
 url           = "https://www.researchgate.net/publication/228924675",
 language      = "english",
 annote        = "There are plenty of known non-trivial properties of circle
                  homeomorphisms. Sometimes, continuity of a circle map may
                  be restrictive in applications. Therefore, the problem of
                  distinguishing a class of circle maps retaining as much
                  properties of homeomorphisms as possible while remaining
                  rather broad is urgent. Clearly, by discarding continuity
                  of a map one inevitably loses some properties inherent to
                  circle homeomorphisms. Nevertheless, as it turned out
                  discontinuous order preserving circle maps retain the
                  majority of symbolic properties of circle homeomorphisms.",
}

@TECHREPORT{Koz:WIAS05,
 author        = "Kozyakin, V. S.",
 title         = "Proof of a Counterexample to the Finiteness Conjecture in
                  the Spirit of the Theory of Dynamical Systems",
 institution   = "Weierstra{\ss}-Institut f{\"u}r Angewandte Analysis und
                  Stochastik",
 address       = "Berlin",
 year          = "2005",
 number        = "1005",
 pagetotal     = "46",
 type          = "Preprint",
 month         = jan,
 doi           = "10.20347/WIAS.PREPRINT.1005",
 url           = "https://www.wias-berlin.de/publications/wias-publ/run.jsp?template=abstract&type=Preprint&year=2005&number=1005",
 language      = "english",
 annote        = "In 1995 J.~C.~Lagarias and Y.~Wang conjectured that the
                  generalized spectral radius of a finite set of square
                  matrices can be attained on a finite product of matrices.
                  The first counterexample to this Finiteness Conjecture was
                  given in 2002 by T.~Bousch and J.~Mairesse and their proof
                  was based on measure-theoretical ideas. In 2003
                  V.~D.~Blondel, J.~Theys and A.~A.~Vladimirov proposed
                  another proof of a counterexample to the Finiteness
                  Conjecture which extensively exploited combinatorial
                  properties of permutations of products of positive
                  matrices. In the paper, it is proposed one more proof of a
                  counterexample of the Finiteness Conjecture fulfilled in a
                  rather traditional manner of the theory of dynamical
                  systems. It is presented description of the structure of
                  trajectories with the maximal growing rate in terms of
                  extremal norms and associated with them so called extremal
                  trajectories. The construction of the counterexample is
                  based on a detailed analysis of properties of extremal
                  norms of two-dimensional positive matrices in which the
                  technique of the Gram symbols is essentially used. At last,
                  notions and properties of the rotation number for
                  discontinuous orientation preserving circle maps play
                  significant role in the proof.",
}

@ARTICLE{Koz:INFOPROC05:e,
 author        = "Kozyakin, V. S.",
 title         = "Rotation numbers of discontinuous orientation-preserving
                  circle maps revisited",
 journal       = "Information Processes",
 year          = "2005",
 volume        = "5",
 number        = "4",
 pages         = "301--335",
 url           = "http://www.jip.ru/2005/283-300.pdf",
 language      = "english",
 annote        = "The theory of circle homeomorphisms has a great number of
                  deep results. However, sometimes continuity or
                  single-valuedness of a circle map may be restrictive in
                  theoretical constructions or applications. In this paper it
                  is shown that some principal properties of circle
                  homeomorphisms are inherited by the class of
                  orientation-preserving circle maps. The latter class is
                  rather broad and contains not only circle homeomorphisms
                  but also a variety of non continuous maps arising in
                  applications. Of course, even in cases when a property
                  remains to be valid for orientation-preserving circle maps,
                  absence of continuity sometimes results in noticeable
                  changes of related proofs.",
}

@ARTICLE{Koz:INFOPROC06:e,
 author        = "Kozyakin, V. S.",
 title         = "Structure of extremal trajectories of discrete linear
                  systems and the finiteness conjecture",
 journal       = "Autom. Remote Control",
 fjournal      = "Automation and Remote Control",
 year          = "2007",
 volume        = "68",
 number        = "1",
 pages         = "174--209",
 issn          = "0005-1179",
 zblnumber     = "1195.93082",
 doi           = "10.1134/S0005117906040171",
 url           = "https://link.springer.com/article/10.1134/S0005117906040171",
 language      = "english",
 annote        = "\emph{J.~C.~Lagarias} and \emph{Y.~Wang} [J. Fourier Anal.
                  Appl. 2, No. 1, 1--14 (1995)] conjectured that the
                  generalized spectral radius of a finite set of square
                  matrices can be attained on a finite product of matrices.
                  The first counterexample to this Finiteness Conjecture was
                  given by \emph{T.~Bousch} and \emph{J.~Mairesse} [J. Am.
                  Math. Soc. 15, No. 1, 77--111 (2002)] and their proof was
                  based on measure-theoretical ideas. \emph{V.~D.~Blondel},
                  \emph{J.~Theys} and \emph{A.~A.~Vladimirov} [SIAM J. Matrix
                  Anal. Appl. 24, No.~4, 963--970 (2003)] proposed another
                  proof of a counterexample to the Finiteness Conjecture
                  which extensively exploited combinatorial properties of
                  permutations of products of positive matrices. In the
                  control theory, so as in the general theory of dynamical
                  systems, the notion of generalized spectral radius is used
                  basically to describe the rate of growth or decrease of the
                  trajectories generated by matrix products. In this context,
                  the above mentioned methods are not enough satisfactory
                  (from the point of view of the author, of course) since
                  they give no description of the structure of the
                  trajectories with the maximal growing rate (or minimal
                  decreasing rate). In connection with this, in 2005 the
                  author [Proof of a counterexample to the finiteness
                  conjecture in the spirit of the theory of dynamical
                  systems, preprint of Weierstra\ss-Institut f{\"u}r
                  Angewandte Analysis und Stochastik, Berlin, No. 105 (2005)]
                  presented one more proof of the counterexample to the
                  Finiteness Conjecture fulfilled in the spirit of the theory
                  of dynamical systems. Unfortunately, the developed approach
                  did not cover the class of matrices considered by Blondel,
                  Theys and Vladimirov. The goal of the present paper is to
                  compensate for this deficiency in the previous approach.",
}

@ARTICLE{Koz:DAN09:e,
 author        = "Kozyakin, V. S.",
 title         = "On the computational aspects of the theory of joint spectral
                  radius",
 journal       = "Dokl. Math.",
 fjournal      = "Doklady Mathematics",
 year          = "2009",
 volume        = "80",
 number        = "1",
 pages         = "487--491",
 issn          = "1064-5624",
 mrclass       = "15A18 (15A60 47A10)",
 mrnumber      = "2573049 (2010k:15023)",
 mrreviewer    = "Adolf Rhodius",
 zblnumber     = "1190.93035",
 doi           = "10.1134/S1064562409040097",
 url           = "https://link.springer.com/article/10.1134/S1064562409040097",
 language      = "english",
 annote        = "One of the most prominent tool to compute the the joint
                  spectral radius of a matrix set is the so-called
                  generalized Gelfand formula which represents the joint
                  spectral radius as a limit of the weighted norms of matrix
                  products with factors taken from the given matrix set.
                  Unfortunately, the range of applicability of this formula
                  is substantially restricted by a lack of estimates for the
                  rate of convergence to the corresponding limit. In the
                  paper this deficiency is made up to some extent. We
                  establish explicit computable estimates of the joint
                  spectral radius by the norms of matrix products with
                  factors taken from the given matrix set, and propose two
                  computational iterative relaxation procedures to
                  approximate the joint spectral radius of matrix sets.",
}

@ARTICLE{Koz:DAN10:e,
 author        = "Kozyakin, V. S.",
 title         = "Polynomial criteria for the {$v$}-sufficiency of jets in
                  classes of finitely smooth mappings",
 journal       = "Dokl. Math.",
 fjournal      = "Doklady Mathematics",
 year          = "2010",
 volume        = "81",
 number        = "1",
 pages         = "101--104",
 issn          = "1064-5624",
 mrclass       = "58Kxx",
 mrnumber      = "2676320",
 zblnumber     = "1213.58003",
 doi           = "10.1134/S106456241001028X",
 url           = "https://link.springer.com/article/10.1134/S106456241001028X",
 language      = "english",
 annote        = "In theory of dynamical systems and nonlinear analysis quite
                  a number of problems depending on parameters require
                  analyzing the structure of the set of solutions of
                  nonlinear equations, the number of variables in which
                  exceeds the number of equations. As a rule, arising
                  equations are rather complicated for investigation and need
                  to be simplified in one or another way. Clearly, such
                  ``simplification'' may lead as to correct conclusions about
                  the structure of solutions as to wrong ones. Often, small
                  solutions of equations are of interest. In this case one of
                  the most popular methods of simplification of equations is
                  their truncation, when one casts out high order terms in
                  power-series expansions of the corresponding equations. In
                  the paper polynomial necessary and sufficient conditions
                  are proved allowing to judge in which cases, in analysis of
                  systems of real nonlinear equations of finite smoothness,
                  truncation is permissible.",
}

@MISC{Koz:ArXiv13,
 author        = "Kozyakin, V. S.",
 title         = "Algebraic Unsolvability of Problem of Absolute Stability of
                  Desynchronized Systems Revisited",
 howpublished  = "ArXiv.org e-Print archive",
 year          = "2013",
 month         = jan,
 eprinttype    = "arXiv",
 eprint        = "1301.5409",
 doi           = "10.48550/arXiv.1301.5409",
 language      = "english",
 annote        = "In the author's article ``Algebraic unsolvability of problem
                  of absolute stability of desynchronized systems'' (Autom.
                  Remote Control 51 (1990), no. 6, pp. 754--759), it was
                  shown that in general for linear desynchronized systems
                  there are no algebraic criteria of absolute stability. In
                  this paper, a few misprints occurred in the original
                  version of the article are corrected, and two figures are
                  added.",
}

@ARTICLE{Koz:INFOPROC15:e,
 author        = "Kozyakin, V. S.",
 title         = "On the asymptotics of cosine series in several variables
                  with power coefficients",
 journal       = "J. Commun. Technol. Electron.",
 fjournal      = "Journal of Communications Technology and Electronics",
 year          = "2015",
 volume        = "60",
 number        = "12",
 pages         = "1441--1444",
 doi           = "10.1134/S1064226915120165",
 language      = "english",
 annote        = "The investigation of the asymptotic behavior of
                  trigonometric series near the origin is a prominent topic
                  in mathematical analysis. For trigonometric series in one
                  variable, this problem was exhaustively studied by various
                  authors in a series of publications dating back to the work
                  of G. H. Hardy, 1928. Trigonometric series in several
                  variables have got less attention. The aim of the work is
                  to find the asymptotics of trigonometric series in several
                  variables with the terms, having a form of ``one minus the
                  cosine'' accurate to a decreasing power factor.",
}

@ARTICLE{Koz:INFOPROC16:e,
 author        = "Kozyakin, V. S.",
 title         = "Constructive stability and stabilizability of positive
                  linear discrete-time switching systems",
 journal       = "J. Commun. Technol. Electron.",
 fjournal      = "Journal of Communications Technology and Electronics",
 year          = "2017",
 volume        = "62",
 number        = "6",
 pages         = "686--693",
 eprinttype    = "arXiv",
 eprint        = "1511.05665",
 doi           = "10.1134/S1064226917060110",
 url           = "https://link.springer.com/article/10.1134/S1064226917060110",
 language      = "english",
 annote        = "We describe a new class of positive linear discrete-time
                  switching systems for which the problems of stability or
                  stabilizability can be resolved constructively. The systems
                  constituting this class can be treated as a natural
                  generalization of systems with the so-called independently
                  switching state vector components. Distinctive feature of
                  such systems is that their components can be arbitrarily
                  ``re-connected'' in parallel or in series without loss of
                  the ``constructive resolvability'' property for the
                  problems of stability or stabilizability of a system. It is
                  shown also that, for such systems, the individual positive
                  trajectories with the greatest or the lowest rate of
                  convergence to the zero can be built constructively.",
}

@ARTICLE{Koz:INFOPROC19:e,
 author        = "Kozyakin, V. S.",
 title         = "Caution, DOI! Bibliographic detective story in the era of
                  digitalization",
 journal       = "J. Commun. Technol. Electron.",
 fjournal      = "Journal of Communications Technology and Electronics",
 year          = "2019",
 volume        = "64",
 number        = "12",
 pages         = "1523--1526",
 eprinttype    = "arXiv",
 eprint        = "1903.03366",
 doi           = "10.1134/S1064226919120076",
 url           = "https://link.springer.com/article/10.1134/S1064226919120076",
 language      = "english",
 annote        = "An example of inconsistencies in information provided by
                  popular bibliographic services is described and the reasons
                  for these inconsistencies are discussed.",
}

@ARTICLE{KozBhaKasz:MCSS99,
 author        = "Kozyakin, V. S. and Bhaya, A. and Kaszkurewicz, E.",
 title         = "A global asymptotic stability result for a class of totally
                  asynchronous discrete nonlinear systems",
 journal       = "Math. Control Signals Systems",
 fjournal      = "Mathematics of Control, Signals, and Systems",
 year          = "1999",
 volume        = "12",
 number        = "2",
 pages         = "143--166",
 coden         = "MCSYE8",
 issn          = "0932-4194",
 mrclass       = "93D15 (39A12 82C32 93C83)",
 mrnumber      = "1692168 (2000d:93058)",
 mrreviewer    = "V{\~u} Ngoc Ph{\'a}t",
 zblnumber     = "0926.93055",
 zblreviewer   = "L.Andrey (Praha)",
 doi           = "10.1007/PL00009848",
 url           = "https://link.springer.com/article/10.1007/PL00009848",
 language      = "english",
 annote        = "This paper proves a global stability result for a class of
                  nonlinear discrete-time systems that are subject to regular
                  desynchronization, also known as total asynchronism. The
                  class of systems studied has its origins in a discrete-time
                  neural net model. The techniques used are of interest in
                  terms of the use of a Lyapunov function for the study of
                  convergence of asynchronous nonlinear dynamical systems and
                  also in terms of applications to neural networks. In the
                  latter context, the main result of this paper strengthens a
                  result of an earlier paper on neural networks, and shows
                  that a class of discrete-time continuous-valued neural nets
                  of the Hopfield type displays global convergence properties
                  even when there exists total asynchronism in the updating
                  of neuron states.",
}

@ARTICLE{KozKraRa:DAN06:e,
 author        = "Kozyakin, V. S. and Krasnosel'skii, A. M. and Rachinskii, D.
                  I.",
 title         = "Arnold tongues in the problem of large-amplitude periodic
                  trajectories",
 journal       = "Dokl. Math.",
 fjournal      = "Doklady Mathematics",
 year          = "2006",
 volume        = "74",
 number        = "3",
 pages         = "821--826",
 issn          = "1064-5624",
 mrclass       = "37G15 (34A26 34C23 34C25)",
 mrnumber      = "2456725 (2010c:37115)",
 mrreviewer    = "Sergei A. Dovbysh",
 zblnumber     = "1205.37065",
 zblreviewer   = "Vladimir P. Kostov (Nice)",
 doi           = "10.1134/S106456240606010X",
 url           = "https://link.springer.com/article/10.1134/S106456240606010X",
 language      = "english",
 annote        = "Consider a finite-dimensional discrete time dynamical system
                  $x_{k+1} =U_{\lambda}x_k$, $x\in\mathbb{R}^{n}$ depending
                  on a complex parameter $\lambda$. In a neighbourhood of an
                  equilibrium (say, at $x_* =0$) its properties are
                  determined by its linear part $A_{\lambda}x$. If the matrix
                  $A_{\lambda}$ has eigenvalues near the unit circle, then in
                  a neighbourhood of $0$ the system may have periodic orbits
                  with different periods. Periodic regimes occur for
                  eigenvalues of the matrix $A_{\lambda}$ from certain
                  domains $U_q$ (with vertices at the points $e^{2\pi qi}$)
                  called Arnold tongues, where $q\in\mathbb{Q}$. The paper
                  studies such tongues at infinity, assuming that the
                  operator $U_{\lambda}$ is of the form $A_{\lambda} x$ +
                  bounded nonlinearity.",
}

@ARTICLE{KozKra:AIT79:e,
 author        = "Kozyakin, V. S. and Krasnosel'skij, M. A.",
 title         = "Influence of small delays on dynamic behavior of nonlinear
                  systems",
 journal       = "Autom. Remote Control",
 fjournal      = "Automation and Remote Control",
 year          = "1979",
 volume        = "40",
 pages         = "1--4",
 issn          = "0005-1179",
 mrclass       = "93C50",
 mrnumber      = "537287 (80j:93077)",
 mrreviewer    = "Pramode K. Bhagat",
 zblnumber     = "0418.93035",
 language      = "english",
}

@ARTICLE{KozKra:ZhVMMF79:e,
 author        = "Kozyakin, V. S. and Krasnosel'skij, M. A.",
 title         = "Some problems connected with the method of minimal
                  residuals",
 journal       = "U.S.S.R. Comput. Math. Math. Phys.",
 fjournal      = "U.S.S.R. Computational Mathematics and Mathematical
                  Physics",
 year          = "1979",
 volume        = "19",
 number        = "2",
 pages         = "244--247",
 issn          = "0041-5553",
 mrclass       = "65F10",
 mrnumber      = "531357 (80b:65045)",
 zblnumber     = "0433.65018",
 doi           = "10.1016/0041-5553(79)90020-X",
 language      = "english",
 annote        = "Two methods are considered for the approximate solution of
                  systems of linear equations $Ax = b$ with asymmetric
                  matrices $A$, the method of successive approximations
                  \[x_{n+1} = x_{n} -\gamma (Ax_{n} - b)\tag{$*$}\] and the
                  method of minimal residuals. An optimal value for the
                  coefficient $\gamma$ in $(*)$ is given for which the
                  sequence $(*)$ converges at the rate of a geometric
                  progression with an explicitely given coefficient $\theta$.
                  The coefficients $\gamma$ and $\theta$ depend on the values
                  $m,u,\varkappa$, for which $m(x,x)\le (Ax,x)\le M(x,x)$,
                  $\|A-A^{*}\|\le 2\varkappa$.",
}

@ARTICLE{KozKra:DAN80:e,
 author        = "Kozyakin, V. S. and Krasnosel'skij, M. A.",
 title         = "The method of parameter functionalization in the problem of
                  bifurcation points",
 journal       = "Sov. Math., Dokl.",
 fjournal      = "Soviet Mathematics. Doklady",
 year          = "1980",
 volume        = "22",
 pages         = "513--517",
 issn          = "0197-6788",
 mrclass       = "47H15 (34K15 58E07)",
 mrnumber      = "592679 (82b:47079)",
 mrreviewer    = "S. Bur{\'y}{\v{s}}ek",
 zblnumber     = "0471.34031",
 language      = "english",
}

@ARTICLE{KozKra:NUMFAO82,
 author        = "Kozyakin, V. S. and Krasnosel'skij, M. A.",
 title         = "Some remarks on the method of minimal residues",
 journal       = "Numer. Funct. Anal. Optim.",
 fjournal      = "Numerical Functional Analysis and Optimization",
 year          = "1982",
 volume        = "4",
 pages         = "211--239",
 issn          = "0163-0563",
 mrclass       = "65F10 (49D07)",
 mrnumber      = "665361 (83h:65043)",
 zblnumber     = "0496.65011",
 doi           = "10.1080/01630568208816115",
 url           = "https://www.tandfonline.com/doi/abs/10.1080/01630568208816115",
 language      = "english",
 annote        = "Two procedures of approximate solution of systems of linear
                  equations with non-symmetric matrices, the method of
                  minimal residues and that of simple iterations, are
                  considered. A comparison of the methods under consideration
                  is made. According to the comparison of the rates of
                  convergence preference should be given to the method of
                  simple iterations. Some arguments are presented
                  nevertheless, in virtue of which, the method of minimal
                  residues should be preferred.",
}

@ARTICLE{KozKra:NA87,
 author        = "Kozyakin, V. S. and Krasnosel'skij, M. A.",
 title         = "The method of parameter functionalization in the {H}opf
                  bifurcation problem",
 journal       = "Nonlinear Anal.",
 fjournal      = "Nonlinear Analysis. Theory, Methods {\&} Applications. An
                  International Multidisciplinary Journal. Series A: Theory
                  and Methods",
 year          = "1987",
 volume        = "11",
 number        = "2",
 pages         = "149--161",
 coden         = "NOANDD",
 issn          = "0362-546X",
 mrclass       = "34C25 (58F14)",
 mrnumber      = "877878 (88b:34052)",
 mrreviewer    = "N. D. Kazarinoff",
 doi           = "10.1016/0362-546X(87)90095-2",
 url           = "https://www.sciencedirect.com/science/article/pii/0362546X87900952",
 language      = "english",
 annote        = "This article contains a topological proof of the Hopf
                  theorem. In this proof the method of parameter
                  functionalization introduced by Krasnosel'skii in another
                  situation, has much significance. Employment of topological
                  considerations makes it possible to throw aside usual
                  assumptions of differentiability of the right-hand member
                  of the parameter-depended system of differential equations
                  under consideration. This provides an opportunity to
                  investigate systems, the right-hand side of which contains,
                  for example, hysteresis-type or relay-type nonlinearities.
                  The proof goes through without changes in the case of
                  functional differential equations with lagging arguments.
                  We do not present the exact formulations of such assertions
                  because our purpose is the demonstration of the method. ln
                  [5,6] the method of parameter functionalization has been
                  applied to the investigation of bifurcation of
                  long-periodic solutions of differential equations and
                  mappings.",
}

@ARTICLE{KozKraPok:DAN72:e,
 author        = "Kozyakin, V. S. and Krasnosel'skij, M. A. and Pokrovskij, A.
                  V.",
 title         = "Vibrationally stable hysterons",
 journal       = "Sov. Math., Dokl.",
 fjournal      = "Soviet Mathematics. Doklady",
 year          = "1972",
 volume        = "13",
 pages         = "1305--1309",
 issn          = "0197-6788",
 mrclass       = "93A10",
 mrnumber      = "0316119 (47 \#4667)",
 mrreviewer    = "Wolfdietrich Muller",
 zblnumber     = "0268.93027",
 language      = "english",
 annote        = "Several properties of a transducer
                  \[x(t)=[W(t_{0},x_{0})u](t)\] with the initial state
                  $(t_{0},x_{0})$ and the control $u(t)$ is studied, when it
                  is static, controlled and proper hysteron. Here a
                  transducer $W(t,x)$ is called to be hysteron if \[[W(t,
                  [W(t_{0},x_{0})u](t))](s) = [W(t_{0},x_{0})u](s)\] for
                  $t_{0}\le t\le s$; to be static if $[W(t_{0},x_{0})u](t)$
                  depends only on $u(t)-u(t_{0})$; to be controlled if for
                  any $(t_{0},x_{0},u_{0})$ and $(x_{1},u_{1})$ we can find a
                  $t_{1}\ge t_{0}$ and $u(t)$ such that \[
                  [W(t_{0},x_{0})u](t_{1})=x_{1},\quad u(t_{0}) = u_{0},\quad
                  u(t_{1}) = u_{1};\] to be proper if, for $u(t)= a +
                  b\,\sin(t -\delta)$, $[W(t_{0},x_{0})u](t)$ is continuous
                  in $(a,b,x_{0})$ uniformly for $t$.",
}

@ARTICLE{KK:INFOPROC07:e,
 author        = "Kozyakin, V. S. and Kuznetsov, N. A.",
 title         = "Feasibility of numerical modelling: Information aspect",
 journal       = "Autom. Remote Control",
 fjournal      = "Automation and Remote Control",
 year          = "2007",
 volume        = "68",
 number        = "12",
 pages         = "2228--2270",
 issn          = "0005-1179",
 zblnumber     = "1148.93004",
 doi           = "10.1134/S0005117907120107",
 url           = "https://link.springer.com/article/10.1134/S0005117907120107",
 language      = "english",
 annote        = "In the paper some problems related to computer studies of
                  continuous objects are considered. Examples are presented
                  which demonstrate that even in trivial situations results
                  of computer modelling can differ drastically from
                  properties of original continuous objects. This observation
                  is aggravated by the fact that often the situation cannot
                  be improved by raise of accuracy of approximating of
                  considered continuous objects. The mathematical models are
                  offered which allow to a certain extent to explain
                  originating phenomena and also to use and/or parry their
                  negative aftereffects.",
}

@ARTICLE{KKCh:AiT19:1:e,
 author        = "Kozyakin, V. S. and Kuznetsov, N. A. and Chebotarev, P.
                  {\relax{}Yu}.",
 title         = "Consensus in asynchronous multiagent systems. I",
 journal       = "Autom. Remote Control",
 fjournal      = "Automation and Remote Control",
 year          = "2019",
 volume        = "80",
 number        = "4",
 pages         = "593--623",
 issn          = "0005-2310",
 mrclass       = "93A14 (93-02 93C15 93Dxx)",
 mrnumber      = "3943136",
 zblnumber     = "1431.93055",
 doi           = "10.1134/S0005117919040015",
 url           = "https://link.springer.com/article/10.1134/S0005117919040015",
 language      = "english",
 annote        = "We present a survey of results on models of consensus in
                  asynchronous multi-agent systems with discrete and
                  continuous time. We consider mathematical methods developed
                  over recent years, which are used in the analysis of
                  stability, stabilization, and consensus problems for linear
                  multi-agent systems with discrete time. These methods are
                  based on the idea of using the notion of joint/generalized
                  spectral radius of a set of matrices to analyze the rate of
                  convergence of matrix products with factors drawn from
                  certain sets of matrices with special properties.",
}

@ARTICLE{KKCh:AiT19:2:e,
 author        = "Kozyakin, V. S. and Kuznetsov, N. A. and Chebotarev, P.
                  {\relax{}Yu}.",
 title         = "Consensus in asynchronous multiagent systems. II",
 journal       = "Autom. Remote Control",
 fjournal      = "Automation and Remote Control",
 year          = "2019",
 volume        = "80",
 number        = "5",
 pages         = "791--812",
 issn          = "0005-2310",
 mrclass       = "93A14 (93-02 93B25 93C15)",
 mrnumber      = "3962445",
 zblnumber     = "1420.93030",
 doi           = "10.1134/S0005117919050011",
 url           = "https://link.springer.com/article/10.1134/S0005117919050011",
 language      = "english",
 annote        = "We describe mathematical methods for analyzing the
                  stability, stabilizability and consensus of linear
                  multiagent systems with discrete time. These methods are
                  based on the idea of using the notion of joint/generalized
                  spectral radius of matrix sets to analyze the rate of
                  convergence of matrix products with factors from the sets
                  of matrices with special properties. This is a continuation
                  of the survey by the same authors named ``Consensus in
                  Asynchronous Multiagent Systems''; the first part was
                  published in~\cite{KKCh:AiT19:1:e}.",
}

@ARTICLE{KKCh:AiT19:3:e,
 author        = "Kozyakin, V. S. and Kuznetsov, N. A. and Chebotarev, P.
                  {\relax{}Yu}.",
 title         = "Consensus in asynchronous multiagent systems. III",
 journal       = "Autom. Remote Control",
 fjournal      = "Automation and Remote Control",
 year          = "2019",
 volume        = "80",
 number        = "6",
 pages         = "989--1014",
 issn          = "0005-2310",
 mrclass       = "93B25 (15A60 37C75 60J20 93-02 93D20)",
 mrnumber      = "3979782",
 zblnumber     = "1431.93056",
 doi           = "10.1134/S0005117919060018",
 url           = "https://link.springer.com/article/10.1134/S0005117919060018",
 language      = "english",
 annote        = "We describe certain classes of linear asynchronous
                  multi-agent systems in discrete time for which the
                  stability problem allows for a constructive solution. We
                  also present a general analytic approach to constructing
                  numerical characteristics similar to the generalized
                  spectral radius in stability theory, which would provide an
                  opportunity to analyze the stabilizability of controlled
                  multi-agent systems. This work completes our survey
                  ``Consensus in asynchronous multi-agent systems,'' whose
                  first two parts have been published
                  in~\cite{KKCh:AiT19:1:e,KKCh:AiT19:2:e}.",
}

@ARTICLE{KKP:IFAC92,
 author        = "Kozyakin, V. S. and Kuznetsov, N. A. and Pokrovskii, A. V.",
 title         = "Influence of Controllability-Type Properties on Reliability
                  and Stability of Desynchronized Systems",
 journal       = "IFAC Proceedings Volumes",
 year          = "1992",
 volume        = "25",
 number        = "8",
 pages         = "392--399",
 keywords      = "controllability; stability; reliability; overshooting;
                  desynchronized system",
 issn          = "1474-6670",
 doi           = "10.1016/S1474-6670(17)54089-6",
 url           = "https://www.sciencedirect.com/science/article/pii/S1474667017540896",
 language      = "english",
 note          = "IFAC Workshop on Automatic Control for Quality and
                  Productivity (ACQP'92), Istanbul, Turkey, 3-5 June 1992",
 annote        = "Systems with high level of failures are considered that
                  permanently operate due to this reason in a transient
                  dynamical regime. In real systems amplitude restrictions
                  for state variables are inevitable and also the so called
                  overshooting effect is inwardly intrinsic. Therefore the
                  operation in transient regime can lead to a great number of
                  secondary failures. At the same time it is known that some
                  classes of the so called desynchronized systems are
                  insensitive to failures in data communication links. In the
                  paper the notion of quasi-controllability for
                  desynchronized systems is introduced that allow easy and
                  efficient to estimate the overshooting measure. This
                  presents the means to design the variety of highly reliable
                  fault-tolerant control and manufacturing systems.",
}

@ARTICLE{KKP:IFAC93,
 author        = "Kozyakin, V. S. and Kuznetsov, N. A. and Pokrovskii, A. V.",
 title         = "Transients in Quasi-Controllable Systems. Overshooting,
                  Stability and Instability",
 journal       = "IFAC Proceedings Volumes",
 year          = "1993",
 volume        = "26",
 number        = "2, Part 4",
 pages         = "871--874",
 keywords      = "controllability; convergence; mathematical system theory;
                  stability; robustness",
 eprinttype    = "arXiv",
 eprint        = "0909.4372",
 issn          = "1474-6670",
 doi           = "10.1016/S1474-6670(17)48596-X",
 url           = "https://www.sciencedirect.com/science/article/pii/S147466701748596X",
 language      = "english",
 note          = "12th Triennal Wold Congress of the International Federation
                  of Automatic control. Volume 4 Applications II, Sydney,
                  Australia, 18-23 July",
 annote        = "Families of regimes for control systems are studied
                  possessing the so called quasi-controllability property
                  that is similar to the Kalman controllability property. A
                  new approach is proposed to estimate the degree of
                  transients overshooting in quasi-controllable systems. This
                  approach is conceptually related with the principle of
                  bounded regimes absence in the absolute stability problem.
                  Its essence is in obtaining of constructive a priori bounds
                  for degree of overshooting in terms of the so called
                  quasi-controllability measure. It is shown that relations
                  between stability, asymptotic stability and instability for
                  quasi-controllable systems are similar to those for systems
                  described by linear differential or difference equations in
                  the case when the leading eigenvalue of the corresponding
                  matrix is simple. The results are applicable for analysis
                  of transients, classical absolute stability problem,
                  stability problem for desynchronized systems and so on.",
}

@ARTICLE{KKP:IFAC94,
 author        = "Kozyakin, V. S. and Kuznetsov, N. A. and Pokrovskii, A. V.",
 title         = "Transients in Quasi--Controllable Systems. {O}vershooting,
                  Stability and Instability",
 journal       = "Control Eng. Practice",
 year          = "1994",
 volume        = "2",
 number        = "6",
 pages         = "1080",
 month         = dec,
 eprinttype    = "arXiv",
 eprint        = "0909.4372",
 doi           = "10.1016/0967-0661(94)91809-0",
 language      = "english",
 annote        = "Families of regimes for control systems are studied
                  possessing the so called quasi-controllability property
                  that is similar to the Kalman controllability property. A
                  new approach is proposed to estimate the degree of
                  transients overshooting in quasi-controllable systems. This
                  approach is conceptually related with the principle of
                  bounded regimes absence in the absolute stability problem.
                  Its essence is in obtaining of constructive a priori bounds
                  for degree of overshooting in terms of the so called
                  quasi-controllability measure. It is shown that relations
                  between stability, asymptotic stability and instability for
                  quasi-controllable systems are similar to those for systems
                  described by linear differential or difference equations in
                  the case when the leading eigenvalue of the corresponding
                  matrix is simple. The results are applicable for analysis
                  of transients, classical absolute stability problem,
                  stability problem for desynchronized systems and so on.",
}

@TECHREPORT{KKP:CADSEM96-006,
 author        = "Kozyakin, V. S. and Kuznetsov, N. A. and Pokrovskii, A. V.",
 title         = "A New Model for Statistics of the First Recurrent Moments
                  and Cycle Lengths in Discretizations of Dynamical Systems",
 institution   = "Deakin University",
 address       = "Geelong, Australia",
 year          = "1996",
 number        = "96--006",
 pagetotal     = "9",
 type          = "CADSEM Report",
 doi           = "10.13140/RG.2.2.35440.87041",
 language      = "english",
 annote        = "A new approach to analysis of a statistical law for the
                  combinatorical characteristics of spatial discretizations
                  of dynamical systems is suggested.",
}

@INPROCEEDINGS{KKP:CESA98,
 author        = "Kozyakin, V. S. and Kuznetsov, N. A. and Pokrovskii, A. V.",
 editor        = "Borne, P. and Ksouri, M. and El Kamel, A.",
 title         = "Quasi-Controllability and Estimates of Amplitudes of
                  Transient Regimes in Discrete Systems",
 booktitle     = "Computational Engineering in Systems Applications,
                  {CESA}'98, April 1--4, 1998",
 publisher     = "Ecole Centrale de Lille, France, CD-ROM",
 organization  = "{IMACS}-{IEEE} Multiconference",
 address       = "Hammamet, Tunisia",
 year          = "1998",
 volume        = "1",
 pages         = "266--271",
 eprinttype    = "arXiv",
 eprint        = "0909.4374",
 isbn          = "2-9512309-0-7",
 language      = "english",
 annote        = "Families of regimes for discrete control systems are studied
                  possessing a special quasi-controllability property that is
                  similar to the Kalman controllability property. A new
                  approach is proposed to estimate the amplitudes of
                  transient regimes in quasi-controllable systems. Its
                  essence is in obtaining of constructive a priori bounds for
                  degree of overshooting in terms of the
                  quasi-controllability measure. The results are applicable
                  for analysis of transients, classical absolute stability
                  problem and, especially, for stability problem for
                  desynchronized systems.",
}

@INPROCEEDINGS{KKV:ECC93,
 author        = "Kozyakin, V. S. and Kuznetsov, N. A. and Vladimirov, A. A.",
 editor        = "Nieuwenhius, J. W. and Praagman, C. and Trentelman, H. L.",
 title         = "The {S}korokhod problem study via desynchronized systems
                  techniques",
 booktitle     = "Proceedings of the European Control Conference {ECC}'93,
                  June 28 -- July 1, 1993",
 publisher     = "European Control Association",
 address       = "Groningen, Netherlands",
 year          = "1993",
 volume        = "2",
 pages         = "760--763",
 isbn          = "978-9-03670-374-1",
 url           = "https://www.researchgate.net/publication/308887257",
 language      = "english",
 annote        = "It is shown that the techniques developed as a tool for the
                  stability analysis of the so called desynchronized discrete
                  event systems may be successfully applied to the
                  investigation of the Skorokhod problem on an orthant in
                  $\mathbb{R}^{N}$. As a result, new conditions for the
                  uniqueness of the Skorokhod problem solution and for the
                  Lipschitz continuity of the corresponding oblique
                  projection mapping are obtained. The robustness of
                  non-uniqueness of the Skorokhod problem solution as well as
                  the robustness of the Lipschitz continuity for the
                  corresponding oblique projection mapping are also
                  established.",
}

@INPROCEEDINGS{KKV:CESA98,
 author        = "Kozyakin, V. S. and Kuznetsov, N. A. and Vladimirov, A. A.",
 editor        = "Borne, P. and Ksouri, M. and El Kamel, A.",
 title         = "Matrix methods in {S}korokhod problems",
 booktitle     = "Computational Engineering in Systems Applications,
                  {CESA}'98, April 1--4, 1998",
 publisher     = "Ecole Centrale de Lille, France, CD-ROM",
 organization  = "{IMACS}-{IEEE} Multiconference",
 address       = "Hammamet, Tunisia",
 year          = "1998",
 volume        = "2",
 pages         = "323--328",
 isbn          = "2-9512309-0-7",
 doi           = "10.13140/2.1.4241.1203",
 url           = "https://www.researchgate.net/publication/234109534",
 language      = "english",
 annote        = "The \emph{Skorokhod problem} is a determined mathematical
                  model used for the construction and analysis of constrained
                  processes, both determined and stochastic, such as queing
                  networks, processor sharing in communication networks,
                  stochastic approximation schemes for problems with
                  constraints, etc. The model we deal with consists of a
                  convex polyhedral set $Z$ in a finite-dimensional space
                  $\mathbb{R}^{n}$ and a family of ``reflection vectors''
                  $d_i$ associated with $(n-1)$-dimensional faces $F_i$ of
                  $Z$. According to certain rules of reflection, an output
                  $x(t)\subseteq Z$ is generated for each continuous input
                  $u(t), u(0)\in Z$. The corresponding input-output operator,
                  if it exists, is called the \emph{Skorokhod map}. The
                  properties of the Skorokhod problem such as existence and
                  uniqueness of an output for any admissible input, and
                  different continuity properties of the associated Skorokhod
                  map can be studied in terms of different types of stability
                  of finite families of special $n\times n$-matrices, namely,
                  the projection matrices onto the hyperplanes $L_i$ parallel
                  to faces $F_i$ along the vectors $d_i$. We present both
                  necessary and sufficient conditions of some of the above
                  properties and also establish new relations between such
                  notions as absolute stability, BV-stability, Perron
                  stability, etc., of finite sets of projections and, more
                  generally, of arbitrary $n\times n$-matrices.",
}

@MISC{KMV:93:e,
 author        = "Kozyakin, V. S. and Mandelbaum, A. and Vladimirov, A. A.",
 title         = "Absolute Stability and Dynamic Complementarity",
 howpublished  = "Institute for Information Transmission Problems RAS,
                  Preprint",
 year          = "1993",
 doi           = "10.13140/RG.2.1.3643.7608/1",
 url           = "http://www.ippi.ru/upload/publications/5800/KMV_E.pdf",
 language      = "english",
 annote        = "The close connection is established between the DCP theory
                  and the absolute stability theory of collections of
                  matrices. The stability methods are implemented to obtain
                  some new results in DCP theory.",
}

@TECHREPORT{KozPok:CADSEM96-005,
 author        = "Kozyakin, V. S. and Pokrovskii, A. V.",
 title         = "Estimates of Amplitudes of Transient Regimes in
                  Quasi-Controllable Discrete Systems",
 institution   = "Deakin University",
 address       = "Geelong, Australia",
 year          = "1996",
 number        = "96--005",
 pagetotal     = "21",
 type          = "CADSEM Report",
 eprinttype    = "arXiv",
 eprint        = "0908.4138",
 language      = "english",
 annote        = "Families of regimes for discrete control systems are studied
                  possessing a special \emph{quasi--con\-troll\-abi\-li\-ty
                  property} that is similar to the Kalman
                  con\-troll\-abi\-li\-ty property. A new approach is
                  proposed to estimate the amplitudes of transient regimes in
                  quasi--controllable systems. Its essence is in obtaining of
                  constructive a priori bounds for degree of overshooting in
                  terms of the quasi--con\-troll\-abi\-li\-ty measure. The
                  results are applicable for analysis of transients,
                  classical absolute stability problem and, especially, for
                  stability problem for desynchronized systems.",
}

@ARTICLE{KozPok:TRANS97,
 author        = "Kozyakin, V. S. and Pokrovskii, A. V.",
 title         = "Quasi-Controllability and Estimation of the Amplitudes of
                  Transient Regimes in Discrete Systems",
 journal       = "Izv., Ross. Akad. Estestv. Nauk, Mat. Mat. Model. Inform.
                  Upr.",
 year          = "1997",
 volume        = "1",
 number        = "3",
 pages         = "128--150",
 zblnumber     = "0911.93017",
 language      = "english",
 note          = "In Russian",
 annote        = "Families of regimes for discrete control systems possessing
                  a special quasi-controllability property that is similar to
                  the Kalman controllability property are studied. A new
                  approach is proposed to estimate the amplitudes of
                  transient regimes in quasi-controllable systems. Its
                  essence is to obtain constructive a priori bounds for the
                  degree of overshooting in terms of the
                  quasi-controllability measure. The results are applicable
                  to the analysis of transients, the classical absolute
                  stability problem and, especially, to the stability problem
                  for desynchronized systems.",
}

@ARTICLE{KozPok:JAMSA01,
 author        = "Kozyakin, V. S. and Pokrovskii, A. V.",
 title         = "The asymptotic behavior of elementary symmetric functions on
                  a probability distribution",
 journal       = "J. Appl. Math. Stochastic Anal.",
 fjournal      = "Journal of Applied Mathematics and Stochastic Analysis",
 year          = "2001",
 volume        = "14",
 number        = "3",
 pages         = "237--248",
 issn          = "1048-9533",
 mrclass       = "05A16 (05C30 60C05)",
 mrnumber      = "1853080 (2002g:05011)",
 mrreviewer    = "Peter J. Grabner",
 zblnumber     = "0983.05009",
 doi           = "10.1155/S1048953301000193",
 url           = "https://www.hindawi.com/journals/ijsa/2001/476764/abs/",
 language      = "english",
 annote        = "The problem on asymptotic of the value $\pi (m,n)=m!\sigma
                  m(p(1,n),p(2,n),\ldots,p(n,n))$ is considered, where
                  $\sigma m(x_{1},x_{2},\ldots,x_{n})$ is the $m$th
                  elementary symmetric function of $n$ variables. The result
                  is interpreted in the context of nonequiprobable random
                  mappings theory.",
}

@ARTICLE{KozPok:DAN92:e,
 author        = "Kozyakin, V. S. and Pokrovskij, A. V.",
 title         = "The role of controllability type properties in the study of
                  asynchronous dynamic systems",
 journal       = "Sov. Phys., Dokl.",
 fjournal      = "Soviet Physics. Doklady",
 year          = "1992",
 volume        = "37",
 number        = "5",
 pages         = "213--215",
 issn          = "0038-5689",
 mrclass       = "93B05 (93C05)",
 mrnumber      = "1198568 (93i:93018)",
 zblnumber     = "0790.93018",
 language      = "english",
 annote        = "Analysis of the stability of so-called synchronous systems
                  has recently attracted considerable attention. In this
                  paper we study the geometric properties of the family of
                  modes for synchronous systems that have special properties
                  of Kalman-controllability type. We show that relations
                  between the properties of stability, asymptotic stability,
                  and instability in the indicated family are analogous to
                  the relations between the corresponding properties for the
                  family of solutions of a linear differential equation or
                  difference equation in the case of simplicity of the
                  leading eigenvalues of the matrices that define these
                  equations. The results stated below are useful for analysis
                  of classical problems on absolute stability. Our approach
                  is similar to the principle of the absence of bounded modes
                  in the problem of absolute stability.",
}

@INPROCEEDINGS{Koz:IMACS97,
 author        = "Kozyakin, Victor",
 editor        = "Lehmann, H. and Rufeger, W. and Sch{\"a}fer, R. P. and
                  Sydow, A.",
 title         = "On Finiteness of Trajectories for One Mapping Associated
                  with Quasi-Inversion of Rotation Mapping on Integer Planar
                  Lattice",
 booktitle     = "15th IMACS World Congress on Scientific Computation,
                  Modelling and Applied Mathematics. Proceedings. Vol. 1.
                  Computational mathematics",
 publisher     = "Wissenschaft und Technik Verlag",
 address       = "Berlin, Germany",
 year          = "1997",
 pages         = "39--44",
 isbn          = "978-3-89685-550-3",
 language      = "english",
 annote        = "Investigation of spatial discretizations, even in simplest
                  cases, is collided with essential difficulties and requires
                  to develop rather non-standard methods. Typical in this
                  respect is the problem of analysis of discretization of the
                  planar rotation mapping which demonstrates that often the
                  behaviour of initial continuous mapping may differ
                  dramatically from that of its discrete counterpart. In the
                  paper it is shown that, while the analysis of discrete
                  analogs of the planar rotation mapping is quite difficult,
                  the pair ``discretization of an original mapping $+$
                  discretization of the inverse mapping'' may have strongly
                  correlated properties.",
}

@INPROCEEDINGS{Koz:ICDEA04,
 author        = "Kozyakin, Victor",
 title         = "A short introduction to asynchronous systems",
 booktitle     = "Proceedings of the {S}ixth {I}nternational {C}onference on
                  {D}ifference {E}quations",
 publisher     = "CRC",
 address       = "Boca Raton, FL",
 year          = "2004",
 pages         = "153--165",
 mrclass       = "93A10 (93D05 93D15)",
 mrnumber      = "2092552 (2005e:93003)",
 zblnumber     = "1083.93032",
 zblreviewer   = "Victor Sharapov (Volgograd)",
 doi           = "10.13140/2.1.1095.3928",
 language      = "english",
 annote        = "Looking at the dynamics of the system described by the
                  equation \[ x(n+1)=f(x(n))\] one may say that coordinates
                  of the vector $x=\{x_{1},x_{2},\ldots,x_{N}\}$ are updated
                  \emph{synchronously}. What happens with the system if
                  coordinates of the vector $x$ are updated
                  \emph{asynchronously}, i.e., if at a given moment $n$ only
                  coordinates with indices $i$ from some set
                  $\omega(n)\subseteq\{1,2,\ldots,N\}$ are changed in
                  accordance with the law \[ x_{i}(n+1)=f_{i}(x(n))\] while
                  others remain intact? This is the main topic which is
                  discussed below.\par Examples of asynchronous systems are
                  multiprocessor systems, distributed digital networks,
                  discrete-time models of market economy, etc.\par The main
                  attention is be paid to discussion of the problem how
                  asynchronism affects stability of the system. Examples show
                  that all possible combinations of stability/instability for
                  the pair `synchronous/asyn\-chro\-nous system' may occur.
                  And also, simple examples demonstrate that the problem of
                  investigation of stability for asynchronous system is more
                  complicate than for synchronous one, even in linear case.
                  Nevertheless, in some situations asynchronous systems
                  possess more robust properties than synchronous ones.\par
                  Formal explanation of this fact is be presented, and
                  various methods of stability investigation for asynchronous
                  system are discussed.",
}

@ARTICLE{Koz:LAA09,
 author        = "Kozyakin, Victor",
 title         = "On accuracy of approximation of the spectral radius by the
                  {G}elfand formula",
 journal       = "Linear Algebra Appl.",
 fjournal      = "Linear Algebra and its Applications",
 year          = "2009",
 volume        = "431",
 number        = "11",
 pages         = "2134--2141",
 eprinttype    = "arXiv",
 eprint        = "0810.2856",
 coden         = "LAAPAW",
 issn          = "0024-3795",
 mrclass       = "15A18 (15A60)",
 mrnumber      = "2567820 (2011c:15033)",
 mrreviewer    = "Fuad Kittaneh",
 zblnumber     = "1177.15012",
 zblreviewer   = "Grozio Stanilov (Sofia)",
 doi           = "10.1016/j.laa.2009.07.008",
 url           = "https://www.sciencedirect.com/science/article/pii/S0024379509003590",
 language      = "english",
 annote        = "The famous Gelfand formula for the spectral radius of a
                  matrix is of great importance in various mathematical
                  constructions. Unfortunately, the range of applicability of
                  this formula is substantially restricted by a lack of
                  estimates for the rate of convergence of the quantities
                  $\|A^{n}\|^{1/n} \to \rho(A)$. In the paper this deficiency
                  is made up to some extent. By using the Bochi inequalities
                  we establish explicit computable estimates for the rate of
                  convergence of the quantities $\|A^{n}\|^{1/n} \to
                  \rho(A)$. The obtained estimates are then extended for
                  evaluation of the joint spectral radius of matrix sets.",
}

@ARTICLE{Koz:LAA10,
 author        = "Kozyakin, Victor",
 title         = "An explicit {L}ipschitz constant for the joint spectral
                  radius",
 journal       = "Linear Algebra Appl.",
 fjournal      = "Linear Algebra and its Applications",
 year          = "2010",
 volume        = "433",
 number        = "1",
 pages         = "12--18",
 eprinttype    = "arXiv",
 eprint        = "0909.3170",
 coden         = "LAAPAW",
 issn          = "0024-3795",
 mrclass       = "15A60 (15A18)",
 mrnumber      = "2645060 (2011e:15042)",
 mrreviewer    = "Susana M. Furtado",
 zblnumber     = "1198.15006",
 zblreviewer   = "Alan L. Andrew (Bundoora)",
 doi           = "10.1016/j.laa.2010.01.028",
 url           = "https://www.sciencedirect.com/science/article/pii/S0024379510000418",
 language      = "english",
 annote        = "\emph{F.~Wirth} [Linear Algebra Appl. 342, 17--40 (2002)]
                  has proved that the joint spectral radius of irreducible
                  compact sets of matrices is locally Lipschitz continuous as
                  a function of the matrix set. In the paper, an explicit
                  formula for the related Lipschitz constant is obtained.",
}

@ARTICLE{Koz:DCDSB10,
 author        = "Kozyakin, Victor",
 title         = "Iterative building of {B}arabanov norms and computation of
                  the joint spectral radius for matrix sets",
 journal       = "Discrete Contin. Dyn. Syst. Ser. B",
 fjournal      = "Discrete and Continuous Dynamical Systems. Series B. A
                  Journal Bridging Mathematics and Sciences",
 year          = "2010",
 volume        = "14",
 number        = "1",
 pages         = "143--158",
 eprinttype    = "arXiv",
 eprint        = "0810.2154",
 issn          = "1531-3492",
 mrclass       = "15A18 (15A60 65F15)",
 mrnumber      = "2644257",
 mrreviewer    = "Panayiotis J. Psarrakos",
 zblnumber     = "1201.65067",
 zblreviewer   = "Georg Hebermehl (Berlin)",
 doi           = "10.3934/dcdsb.2010.14.143",
 url           = "https://www.aimsciences.org/article/doi/10.3934/dcdsb.2010.14.143",
 language      = "english",
 annote        = "An extremal norm satisfying the theorem\par \emph{Let the,
                  matrix set $\mathcal{A} = \{A_1,\ldots,A_r\}$ be
                  irreducible. Then the quantity $\rho$ is the joint
                  (generalized) spectral radius of $\mathcal{A}$ if and only
                  if there exist a norm $\|\cdot\|$ in $\mathbb{R}^m$ such
                  that $\rho\|x\| = \max\{\|A_1 x\|\}, \{\| A_2 x
                  \|,\ldots,\| A_r x \|\}$.}\par is called a Barabanov norm
                  [\emph{N.~E.~Barabanov}, ``Lyapunov indicator of discrete
                  inclusions. I--III'', Autom. Remote Control 49, No.~2,
                  152--157 (1988), No. 3, 283--287 (1988), No.~5,558--565
                  (1988)].\par The author used this norm in earlier papers
                  [e.g., \emph{V.~Kozyakin}, ``Structure of extremal
                  trajectories of discrete linear systems and the finiteness
                  conjecture'', Autom. Remote Control 68, No.~1, 174--209
                  (2007)], to disprove the Lagarias-Wang finiteness
                  conjecture \emph{J.~C.~Lagarias} and \emph{Y.~Wang} [J.
                  Fourier Anal. Appl. 2, No.~1, 1--14 (1995)]. The
                  geometrical properties of the unit balls of specific
                  Barabanov norms play a decisive role in the corresponding
                  constructions and in other applications.\par Because the
                  Barabanov norms are only defined by an implicit procedure
                  it is very difficult to visualize the shapes of the related
                  unit balls. Thus, in the present work an iteration
                  procedure is created that allows to build Barabanov norms
                  for irreducible matrix sets. Simultaneously the joint
                  spectral radius of these sets is computed. The convergence
                  of the iteration is formulated in a main theorem and proved
                  with the help of some lemmas. Computational errors of the
                  joint spectral radius can be a posteriori determined. The
                  algorithm is demonstrated by two examples. The
                  corresponding computed unit spheres are shown in figures.
                  Some open problems about the accuracy of the Barabanov
                  norm, about the convergence rate of the joint spectral
                  radius and other are formulated at the end of the paper.",
}

@MISC{Koz:ArXiv10-1,
 author        = "Kozyakin, Victor",
 title         = "Max-{R}elaxation Iteration Procedure for Building of
                  {B}arabanov Norms: Convergence and Examples",
 howpublished  = "ArXiv.org e-Print archive",
 year          = "2010",
 month         = feb,
 eprinttype    = "arXiv",
 eprint        = "1002.3251",
 doi           = "10.48550/arXiv.1002.3251",
 language      = "english",
 annote        = "The problem of construction of Barabanov norms for analysis
                  of properties of the joint (generalized) spectral radius of
                  matrix sets has been discussed in a number of publications.
                  In earlier author's works the method of Barabanov norms was
                  the key instrument in disproving the Lagarias-Wang
                  Finiteness Conjecture. The related constructions were
                  essentially based on the study of the geometrical
                  properties of the unit balls of some specific Barabanov
                  norms. In this context the situation when one fails to find
                  among current publications any detailed analysis of the
                  geometrical properties of the unit balls of Barabanov norms
                  looks a bit paradoxical. Partially this is explained by the
                  fact that Barabanov norms are defined nonconstructively, by
                  an implicit procedure. So, even in simplest cases it is
                  very difficult to visualize the shape of their unit balls.
                  The present work may be treated as the first step to make
                  up this deficiency. In the paper an iteration procedure is
                  considered that allows to build numerically Barabanov norms
                  for the irreducible matrix sets and simultaneously to
                  compute the joint spectral radius of these sets.",
}

@ARTICLE{Koz:DEDS10,
 author        = "Kozyakin, Victor",
 title         = "On explicit a priori estimates of the joint spectral radius
                  by the generalized {G}elfand formula",
 journal       = "Differ. Equ. Dyn. Syst.",
 fjournal      = "Differential Equations and Dynamical Systems",
 year          = "2010",
 volume        = "18",
 number        = "1-2",
 pages         = "91--103",
 eprinttype    = "arXiv",
 eprint        = "0810.2157",
 issn          = "0971-3514",
 mrclass       = "15A18 (47A10 93D20)",
 mrnumber      = "2670076 (2011f:15032)",
 mrreviewer    = "Janko Bra{\v{c}}i{\v{c}}",
 zblnumber     = "1219.15019",
 zblreviewer   = "Marjeta Kramar Fijav{\v{z}} (Ljubljana)",
 doi           = "10.1007/s12591-010-0010-1",
 url           = "https://link.springer.com/article/10.1007/s12591-010-0010-1",
 language      = "english",
 annote        = "In various problems of control theory, non-autonomous and
                  multivalued dynamical systems, wavelet theory and other
                  fields of mathematics information about the rate of growth
                  of matrix products with factors taken from some matrix set
                  plays a key role. One of the most prominent quantities
                  characterizing the exponential rate of growth of matrix
                  products is the so-called joint or generalized spectral
                  radius. In the work some explicit a priori estimates for
                  the joint spectral radius with the help of the generalized
                  Gelfand formula are obtained. These estimates are based on
                  the notion of the measure of irreducibility
                  (quasi-controllability) of matrix sets previously
                  introduced and investigated by \emph{V.~S.~Kozyakin} and
                  \emph{A.~V.~Pokrovskii} [Sov. Phys., Dokl. 37, No.~5,
                  213--215 (1992); Izv., Ross. Akad. Estestv. Nauk, Mat. Mat.
                  Model. Inform. Upr. 1, No.~3, 128--150 (1997)].",
}

@ARTICLE{Koz:DCDSB10-2,
 author        = "Kozyakin, Victor",
 title         = "Polynomial reformulation of the {K}uo criteria for
                  {$V$}-sufficiency of map-germs",
 journal       = "Discrete Contin. Dyn. Syst. Ser. B",
 fjournal      = "Discrete and Continuous Dynamical Systems. Series B. A
                  Journal Bridging Mathematics and Sciences",
 year          = "2010",
 volume        = "14",
 number        = "2",
 pages         = "587--602",
 eprinttype    = "arXiv",
 eprint        = "0907.0571",
 issn          = "1531-3492",
 mrclass       = "58Kxx",
 mrnumber      = "2660873",
 zblnumber     = "1207.58030",
 doi           = "10.3934/dcdsb.2010.14.587",
 url           = "https://www.aimsciences.org/article/doi/10.3934/dcdsb.2010.14.587",
 language      = "english",
 annote        = "In the paper a set of necessary and sufficient conditions
                  for v-sufficiency (equiv. sv-sufficiency) of jets of
                  map-germs is proved which generalize both the Kuiper-Kuo
                  and the Thom conditions in the function case ($m=1$) so as
                  the Kuo conditions in the general map case ($m>1$).
                  Contrary to the Kuo conditions the conditions proved in the
                  paper do not require to verify any inequalities in a
                  so-called horn-neighborhood of the (a'priori unknown) set
                  $f^{-1}(0)$. Instead, the proposed conditions reduce the
                  problem on v-sufficiency of jets to evaluating the local
                  Lojasiewicz exponents for some constructively built
                  polynomial functions.",
}

@ARTICLE{Koz:JDEA11,
 author        = "Kozyakin, Victor",
 title         = "A relaxation scheme for computation of the joint spectral
                  radius of matrix sets",
 journal       = "J. Differ. Equations Appl.",
 fjournal      = "Journal of Difference Equations and Applications",
 year          = "2011",
 volume        = "17",
 number        = "2",
 pages         = "185--201",
 eprinttype    = "arXiv",
 eprint        = "0810.4230",
 issn          = "1023-6198",
 mrclass       = "15A18 (15A60 65F15)",
 mrnumber      = "2783343 (2012e:15021)",
 mrreviewer    = "Panayiotis J. Psarrakos",
 zblnumber     = "1214.65015",
 zblreviewer   = "Constantin Popa (Constan{\c{t}}a)",
 doi           = "10.1080/10236198.2010.549008",
 url           = "https://www.tandfonline.com/doi/abs/10.1080/10236198.2010.549008",
 language      = "english",
 annote        = "The problem of computation of the joint (generalized)
                  spectral radius of matrix sets has been discussed in a
                  number of publications. In this paper, an iteration
                  procedure is proposed that allows to build numerically
                  Barabanov norms for the irreducible matrix sets and
                  simultaneously to compute the joint spectral radius of
                  these sets.",
}

@TECHREPORT{Koz:IITP13,
 author        = "Kozyakin, Victor",
 title         = "An annotated bibliography on the convergence of matrix
                  products and the theory of joint/generalized spectral
                  radius",
 institution   = "Institute for Information Transmission Problems",
 address       = "Moscow",
 year          = "2013",
 pagetotal     = "73",
 type          = "Preprint",
 month         = dec,
 doi           = "10.13140/RG.2.1.4257.5040/1",
 url           = "https://kozyakin.github.io/jsrbib/JSRbib.html",
 language      = "english",
 annote        = "In this work, an attempt is undertaken to list publications
                  on convergence of infinite matrix products and the rate of
                  their growth/decrease when the number of multipliers tends
                  to infinity.",
}

@ARTICLE{Koz:LAA14-2,
 author        = "Kozyakin, Victor",
 title         = "Matrix products with constraints on the sliding block
                  relative frequencies of different factors",
 journal       = "Linear Algebra Appl.",
 fjournal      = "Linear Algebra and its Applications",
 year          = "2014",
 volume        = "457",
 pages         = "244--260",
 month         = sep,
 eprinttype    = "arXiv",
 eprint        = "1403.5050",
 issn          = "0024-3795",
 mrclass       = "15A60 (37B10 60J10)",
 mrnumber      = "3230443",
 zblnumber     = "1291.15027",
 doi           = "10.1016/j.laa.2014.05.016",
 url           = "https://www.sciencedirect.com/science/article/pii/S0024379514002961",
 language      = "english",
 annote        = "One of fundamental results of the theory of
                  joint/generalized spectral radius, the Berger-Wang theorem,
                  establishes equality between the joint and generalized
                  spectral radii of a set of matrices. Generalization of this
                  theorem on products of matrices whose factors are applied
                  not arbitrarily but are subjected to some constraints is
                  connected with essential difficulties since known proofs of
                  the Berger-Wang theorem rely on the arbitrariness of
                  appearance of different matrices in the related matrix
                  products. Recently, X.~Dai [\emph{Robust periodic stability
                  implies uniform exponential stability of Markovian jump
                  linear systems and random linear ordinary differential
                  equations}, J. Franklin Inst. 351 (2014), no. 5,
                  2910--2937] proved an analog of the Berger-Wang theorem for
                  the case when factors in matrix products are formed by some
                  Markov law.\par We introduce the concepts of the joint and
                  generalized spectral radii for products of matrices
                  subjected to constraints on the sliding block relative
                  frequencies of occurrences of different matrices, and prove
                  an analog of the Berger-Wang theorem for this case.",
}

@ARTICLE{Koz:LAA14,
 author        = "Kozyakin, Victor",
 title         = "The {B}erger-{W}ang formula for the {M}arkovian joint
                  spectral radius",
 journal       = "Linear Algebra Appl.",
 fjournal      = "Linear Algebra and its Applications",
 year          = "2014",
 volume        = "448",
 pages         = "315--328",
 month         = may,
 eprinttype    = "arXiv",
 eprint        = "1401.2711",
 issn          = "0024-3795",
 mrclass       = "15A60 (60J20)",
 mrnumber      = "3182989",
 mrreviewer    = "Jaros{\l}aw Adam Miszczak",
 zblnumber     = "06278067",
 doi           = "10.1016/j.laa.2014.01.022",
 url           = "https://www.sciencedirect.com/science/article/pii/S0024379514000408",
 language      = "english",
 annote        = "The Berger-Wang formula establishes equality between the
                  joint and generalized spectral radii of a set of matrices.
                  For matrix products whose multipliers are applied not
                  arbitrarily but in accordance to some Markovian law, there
                  are also known analogs of the joint and generalized
                  spectral radii. However, the known proofs of the
                  Berger-Wang formula hardly can be directly applied in the
                  case of Markovian products of matrices since they
                  essentially rely on the arbitrariness of appearance of
                  different matrices in the related matrix products.
                  Nevertheless, as has been shown by X.~Dai [\emph{Robust
                  periodic stability implies uniform exponential stability of
                  Markovian jump linear systems and random linear ordinary
                  differential equations}, J. Franklin Inst. 351 (2014), no.
                  5, 2910--2937] the Berger-Wang formula is valid for the
                  case of Markovian analogs of the joint and the generalized
                  spectral radii too, although the proof in this case heavily
                  exploits the more involved techniques of multiplicative
                  ergodic theory. In the paper we propose a matrix theory
                  construction allowing deduce the Markovian analog of the
                  Berger-Wang formula from the classical Berger-Wang
                  formula.",
}

@ARTICLE{Koz:IJARM16,
 author        = "Kozyakin, Victor",
 title         = "Hardy type asymptotics for cosine series in several
                  variables with decreasing power-like coefficients",
 journal       = "International Journal of Advanced Research in Mathematics",
 year          = "2016",
 volume        = "5",
 pages         = "35--51",
 month         = jun,
 keywords      = "trigonometric series in several variables; power-like
                  coefficients; decreasing coefficients; asymptotic behavior
                  at zero; {H}ardy type asymptotics",
 eprinttype    = "arXiv",
 eprint        = "1409.1851",
 doi           = "10.18052/www.scipress.com/IJARM.5.35",
 url           = "https://www.scipress.com/IJARM.5.35",
 language      = "english",
 annote        = "The investigation of the asymptotic behavior of
                  trigonometric series near the origin is a prominent topic
                  in mathematical analysis. For trigonometric series in one
                  variable, this problem was exhaustively studied by various
                  authors in a series of publications dating back to the work
                  of G. H. Hardy, 1928. Trigonometric series in several
                  variables have got less attention. The aim of the work is
                  to partially fill this gap by finding the asymptotics of
                  trigonometric series in several variables with the terms,
                  having a form of `one minus the cosine' up to a decreasing
                  power-like factor:
                  \[\sum_{z\in\mathbb{Z}^{d}\setminus\{0\}}
                  \frac{1}{\|z\|^{d+\alpha}}\left(1-\cos\langle
                  z,\theta\rangle\right), \qquad \theta\in\mathbb{R}^{d},\]
                  where $\langle\cdot,\cdot\rangle$ is the standard inner
                  product and $\|\cdot\|$ is the max-norm on
                  $\mathbb{R}^{d}$. The approach developed in the paper is
                  quite elementary and essentially algebraic. It does not
                  rely on the classic machinery of the asymptotic analysis
                  such as slowly varying functions, Tauberian theorems or the
                  Abel transform. However, in our case, it allows to obtain
                  explicit expressions for the asymptotics and to extend to
                  the general case $d\ge 1$ classical results of G. H. Hardy
                  and other authors known for $d=1$.",
}

@CONFERENCE{Koz:WSDV16,
 author        = "Kozyakin, Victor",
 title         = "Hourglass Alternative and constructivity of spectral
                  characteristics of matrix products",
 booktitle     = "Workshop on switching dynamics {\&} verification, January
                  28-29",
 organization  = "Institut pour le Contr{\^o}le et la D{\'e}cision de l'Idex
                  Paris-Saclay, Paris, France",
 year          = "2016",
 doi           = "10.13140/RG.2.1.4880.1042",
 url           = "http://www.cmap.polytechnique.fr/~sdv2016/slides/kozyakin_SDV2016.pdf",
 language      = "english",
 annote        = "Recently Blondel, Nesterov and Protasov proved that the
                  finiteness conjecture holds for the generalized and the
                  lower spectral radii of the sets of non-negative matrices
                  with independent row/column uncertainty. We show that this
                  result can be obtained as a simple consequence of the
                  so-called hourglass alternative which can be used also to
                  establish the minimax relations between the spectral radii
                  of matrix products. Axiomatization of the statements that
                  constitute the hourglass alternative makes it possible to
                  define a new class of sets of positive matrices having the
                  finiteness property, which includes the sets of
                  non-negative matrices with independent row uncertainty.
                  This class of matrices, supplemented by the zero and
                  identity matrices, forms a semiring with the Minkowski
                  operations of addition and multiplication of matrix sets,
                  which gives means to construct new sets of non-negative
                  matrices possessing the finiteness property for the
                  generalized and the lower spectral radii.\par The Hourglass
                  alternative helps us to describe a new class of positive
                  linear discrete-time switching systems for which the
                  problems of stability or stabilizability can be resolved
                  constructively. This class generalizes the class of systems
                  with independently switching state vector components. The
                  distinctive feature of this class is that, for any system
                  from this class, its components or blocks can be
                  arbitrarily connected in parallel or in series without loss
                  of the `constructive resolvability' property. It is shown
                  also that, for such systems, it is possible to build
                  constructively the individual positive trajectories with
                  the greatest or the lowest rate of convergence to the
                  zero.",
}

@ARTICLE{Koz:LAA16,
 author        = "Kozyakin, Victor",
 title         = "Hourglass alternative and the finiteness conjecture for the
                  spectral characteristics of sets of non-negative matrices",
 journal       = "Linear Algebra Appl.",
 fjournal      = "Linear Algebra and its Applications",
 year          = "2016",
 volume        = "489",
 pages         = "167--185",
 keywords      = "matrix products; non-negative matrices; joint spectral
                  radius; lower spectral radius; finiteness conjecture",
 eprinttype    = "arXiv",
 eprint        = "1507.00492",
 coden         = "LAAPAW",
 issn          = "0024-3795",
 mrclass       = "15A18 (15B48, 15A60)",
 mrnumber      = "3421844",
 zblnumber     = "1326.15053",
 doi           = "10.1016/j.laa.2015.10.017",
 url           = "https://www.sciencedirect.com/science/article/pii/S0024379515006126",
 language      = "english",
 annote        = "Recently Blondel, Nesterov and Protasov proved that the
                  finiteness conjecture holds for the generalized and the
                  lower spectral radii of the sets of non-negative matrices
                  with independent row/column uncertainty. We show that this
                  result can be obtained as a simple consequence of the
                  so-called hourglass alternative earlier used by the author
                  and his companions to analyze the minimax relations between
                  the spectral radii of matrix products. Axiomatization of
                  the statements that constitute the hourglass alternative
                  makes it possible to define a new class of sets of positive
                  matrices having the finiteness property, which includes the
                  sets of non-negative matrices with independent row
                  uncertainty. This class of matrices, supplemented by the
                  zero and identity matrices, forms a semiring with the
                  Minkowski operations of addition and multiplication of
                  matrix sets, which gives means to construct new sets of
                  non-negative matrices possessing the finiteness property
                  for the generalized and the lower spectral radii.",
}

@ARTICLE{Koz:LMA17,
 author        = "Kozyakin, Victor",
 title         = "Minimax theorem for the spectral radius of the product of
                  non-negative matrices",
 journal       = "Linear Multilinear Algebra",
 fjournal      = "Linear and Multilinear Algebra",
 year          = "2017",
 volume        = "65",
 number        = "11",
 pages         = "2356--2365",
 eprinttype    = "arXiv",
 eprint        = "1603.05375",
 issn          = "0308-1087",
 mrclass       = "15A45 (15A60 15B48 49J35)",
 mrnumber      = "3740702",
 mrreviewer    = "Jaspal Singh Aujla",
 zblnumber     = "1387.15017",
 doi           = "10.1080/03081087.2016.1273877",
 url           = "https://www.tandfonline.com/doi/full/10.1080/03081087.2016.1273877",
 language      = "english",
 annote        = "We prove the minimax equality for the spectral radius
                  $\rho(AB)$ of the product of matrices $A\in\mathcal{A}$ and
                  $B\in\mathcal{B}$, where $\mathcal{A}$ and $\mathcal{B}$
                  are compact sets of non-negative matrices of dimensions
                  $N\times M$ and $M\times N$, respectively, satisfying the
                  so-called hourglass alternative.",
}

@ARTICLE{Koz:DDNS18,
 author        = "Kozyakin, Victor",
 title         = "On convergence of infinite matrix products with alternating
                  factors from two sets of matrices",
 journal       = "Discrete Dyn. Nat. Soc.",
 fjournal      = "Discrete Dynamics in Nature and Society. An International
                  Multidisciplinary Research and Review Journal",
 year          = "2018",
 volume        = "Art. ID 9216760",
 pages         = "1--5",
 keywords      = "matrix products; alternating factors from two sets of
                  matrices",
 eprinttype    = "arXiv",
 eprint        = "1712.06356",
 issn          = "1026-0226",
 mrclass       = "93D20 (15A60 40A20)",
 mrnumber      = "3798756",
 mrreviewer    = "Roksana Krystyna S\l owik",
 zblnumber     = "1417.93254",
 doi           = "10.1155/2018/9216760",
 url           = "https://www.hindawi.com/journals/ddns/2018/9216760",
 language      = "english",
 annote        = "We consider the problem of convergence to zero of matrix
                  products $A_{n}B_{n}\cdots A_{1}B_{1}$ with factors from
                  two sets of matrices, $A_{i}\in\mathcal{A}$ and
                  $B_{i}\in\mathcal{B}$, due to a suitable choice of matrices
                  $\{B_{i}\}$. It is assumed that for any sequence of
                  matrices $\{A_{i}\}$ there is a sequence of matrices
                  $\{B_{i}\}$ such that the corresponding matrix product
                  $A_{n}B_{n}\cdots A_{1}B_{1}$ converges to zero. We show
                  that in this case the convergence of the matrix products
                  under consideration is uniformly exponential, that is,
                  $\|A_{n}B_{n}\cdots A_{1}B_{1}\|\le C\lambda^{n}$, where
                  the constants $C>0$ and $\lambda\in(0,1)$ do not depend on
                  the sequence $\{A_{i}\}$ and the corresponding sequence
                  $\{B_{i}\}$.\par Other problems of this kind are discussed
                  and open questions are formulated.",
}

@ARTICLE{Koz:DCDSB19,
 author        = "Kozyakin, Victor",
 title         = "Minimax joint spectral radius and stabilizability of
                  discrete-time linear switching control systems",
 journal       = "Discrete Contin. Dyn. Syst. Ser. B",
 fjournal      = "Discrete and Continuous Dynamical Systems. Series B. A
                  Journal Bridging Mathematics and Sciences",
 year          = "2019",
 volume        = "24",
 number        = "8",
 pages         = "3537--3556",
 keywords      = "minimax; joint spectral; radius; stabilizability; switching
                  systems; discrete-time systems",
 eprinttype    = "arXiv",
 eprint        = "1712.06805",
 issn          = "1531-3492",
 mrclass       = "93D15 (15A18 93B25 93C30 93C55 94C11)",
 mrnumber      = "3986244",
 zblnumber     = "1427.93180",
 doi           = "10.3934/dcdsb.2018277",
 url           = "https://aimsciences.org/article/doi/10.3934/dcdsb.2018277",
 language      = "english",
 annote        = "To estimate the growth rate of matrix products $A_{n}\cdots
                  A_{1}$ with factors from some set of matrices
                  $\mathscr{A}$, such numeric quantities as the joint
                  spectral radius $\rho(\mathscr{A})$ and the lower spectral
                  radius $\check{\rho}(\mathscr{A})$ are traditionally used.
                  The first of these quantities characterizes the maximum
                  growth rate of the norms of the corresponding products,
                  while the second one characterizes the minimal growth rate.
                  In the theory of discrete-time linear switching systems,
                  the inequality $\rho(\mathscr{A})<1$ serves as a criterion
                  for the stability of a system, and the inequality
                  $\check{\rho}(\mathscr{A})<1 $ as a criterion for
                  stabilizability.\par For matrix products $A_{n}B_{n}\cdots
                  A_{1}B_{1}$ with factors $A_{i}\in\mathscr{A}$ and
                  $B_{i}\in\mathscr{B}$, where $\mathscr{A}$ and
                  $\mathscr{B}$ are some sets of matrices, we introduce the
                  quantities $\mu(\mathscr{A},\mathscr{B})$ and
                  $\eta(\mathscr{A},\mathscr{B})$, called the lower and upper
                  minimax joint spectral radius of the pair
                  $\{\mathscr{A},\mathscr{B}\}$, respectively, which
                  characterize the maximum growth rate of the matrix products
                  $A_{n}B_{n}\cdots A_{1}B_{1}$ over all sets of matrices
                  $A_{i}\in\mathscr{A}$ and the minimal growth rate over all
                  sets of matrices $B_{i}\in\mathscr{B}$. In this sense, the
                  minimax joint spectral radii can be considered as
                  generalizations of both the joint and lower spectral radii.
                  As an application of the minimax joint spectral radii, it
                  is shown how these quantities can be used to analyze the
                  stabilizability of discrete-time linear switching control
                  systems in the presence of uncontrolled external
                  disturbances of the plant.",
}

@MISC{Koz:ArXiv20,
 author        = "Kozyakin, Victor",
 title         = "On the boundedness of infinite matrix products with
                  alternating factors from two sets of matrices",
 howpublished  = "ArXiv.org e-Print archive",
 year          = "2020",
 month         = oct,
 eprinttype    = "arXiv",
 eprint        = "2010.03890",
 doi           = "10.48550/arXiv.2010.03890",
 language      = "english",
 annote        = "We consider the question of boundedness of matrix products
                  $A_{n}B_{n}\cdots A_{1}B_{1}$ with factors from two sets of
                  matrices, $A_{i}\in\mathcal{A}$ and $B_{i}\in\mathcal{B}$,
                  due to an appropriate choice of matrices $\{B_{i}\}$. It is
                  assumed that for every sequence of matrices $\{A_{i}\}$
                  there is a sequence of matrices $\{B_{i}\}$ for which the
                  sequence of matrix products $\{A_{n}B_{n}\cdots
                  A_{1}B_{1}\}_{n=1}^{\infty}$ is norm bounded. Some
                  situations are described where in this case the norms of
                  the matrix products $A_{n}B_{n}\cdots A_{1}B_{1}$ are
                  uniformly bounded, that is, $\|A_{n}B_{n}\cdots
                  A_{1}B_{1}\|\le C$ for all natural numbers $n$, where $C >
                  0$ is a constant independent of the sequence $\{A_{i}\}$
                  and the corresponding sequence $\{B_{i}\}$. For the general
                  case, the question of the validity of the corresponding
                  statement remains open.",
}

@ARTICLE{Koz:Automatica22,
 author        = "Kozyakin, Victor",
 title         = "Non-{S}turmian sequences of matrices providing the maximum
                  growth rate of matrix products",
 journal       = "Automatica J. IFAC",
 fjournal      = "Automatica. A Journal of IFAC, the International Federation
                  of Automatic Control",
 year          = "2022",
 volume        = "145",
 pages         = "Paper No. 110574, 10",
 month         = nov,
 eprinttype    = "arXiv",
 eprint        = "2112.00391",
 issn          = "0005-1098",
 mrclass       = "15A60 (37C35 93C05 93C30)",
 mrnumber      = "4473668",
 zblnumber     = "07595547",
 doi           = "10.1016/j.automatica.2022.110574",
 url           = "https://www.sciencedirect.com/science/article/pii/S0005109822004356",
 language      = "english",
 annote        = "In the theory of linear switching systems with discrete
                  time, as in other areas of mathematics, the problem of
                  studying the growth rate of the norms of all possible
                  matrix products $A_{\sigma_{n}}\cdots A_{\sigma_{0}}$ with
                  factors from a set of matrices $\mathcal{A}$ arises. So
                  far, only for a relatively small number of classes of
                  matrices $\mathcal{A}$ has it been possible to accurately
                  describe the sequences of matrices that guarantee the
                  maximum rate of increase of the corresponding norms.
                  Moreover, in almost all cases studied theoretically, the
                  index sequences $\{\sigma_{n}\}$ of matrices maximizing the
                  norms of the corresponding matrix products have been shown
                  to be periodic or so-called Sturmian, which entails a whole
                  set of ``good'' properties of the sequences
                  $\{A_{\sigma_{n}}\}$, in particular the existence of a
                  limiting frequency of occurrence of each matrix factor
                  $A_{i}\in\mathscr{A}$ in them. In the paper it is shown
                  that this is not always the case: a class of matrices is
                  defined consisting of two $2\times 2$ matrices, similar to
                  rotations in the plane, in which the sequence
                  $\{A_{\sigma_{n}}\}$ maximizing the growth rate of the
                  norms $\|A_{\sigma_{n}}\cdots A_{\sigma_{0}}\|$ is not
                  Sturmian. All considerations are based on numerical
                  modeling and cannot be considered mathematically rigorous
                  in this part; rather, they should be interpreted as a set
                  of questions for further comprehensive theoretical
                  analysis.",
}

@ARTICLE{Koz:INFOPROC23:e,
 author        = "Kozyakin, Victor",
 title         = "Bibliography converter from BibTEX format to AMSBIB format",
 journal       = "Information Processes.",
 year          = "2023",
 volume        = "23",
 number        = "4",
 pages         = "455--469",
 url           = "http://www.jip.ru/2023/455-469-2023.pdf",
 language      = "english",
 note          = "in Russian",
 annote        = "A system for converting bibliography from the Bib\TeX{}
                  format into the AMSBIB format, recommended by the Russian
                  portal Math-Net.Ru for use in preparing bibliographies in
                  publications for Russian mathematical journals, is
                  described. Carrying out such a transformation comes down to
                  using the standard procedure for creating a bibliography
                  with the Bib\TeX{} system.",
}

@MISC{Koz:ArXiv24,
 author        = "Victor Kozyakin",
 title         = "On sets of matrices having different spectrum maximizing
                  products with unequal numbers of the same name factors",
 howpublished  = "ArXiv.org e-Print archive",
 year          = "2024",
 month         = jul,
 eprinttype    = "arXiv",
 eprint        = "2407.10513",
 doi           = "10.48550/arXiv.2407.10513",
 language      = "english",
 annote        = "Recently, J.~Bochi and P.~Laskawiec constructed an example
                  of a set of matrices $\{A,B\}$ having two different (up to
                  cyclic permutations of factors) spectrum maximizing
                  products, $AABABB$ and $BBABAA$. In this paper, we identify
                  a class of matrix sets for which the existence of at least
                  one spectrum maximizing product with an odd number of
                  factors automatically entails the existence of another
                  spectrum maximizing product. Moreover, in addition to
                  Bochi--Laskawiec's example, the number of factors of the
                  same name (factors of the form $A$ or $B$) in these matrix
                  products turns out to be different. The efficiency of the
                  proposed approach is confirmed by constructing an example
                  of a set of $2\times2$ matrices $\{A,B\}$ that has spectrum
                  maximizing products of the form $BAA$ and $BBA$.",
}

@ARTICLE{KozKraRa:DCDSA08,
 author        = "Kozyakin, Victor and Krasnosel'skii, Alexander and
                  Rachinskii, Dmitrii",
 title         = "Asymptotics of the {A}rnold tongues in problems at
                  infinity",
 journal       = "Discrete Contin. Dyn. Syst.",
 fjournal      = "Discrete and Continuous Dynamical Systems. Series A",
 year          = "2008",
 volume        = "20",
 number        = "4",
 pages         = "989--1011",
 issn          = "1078-0947",
 mrclass       = "37G15 (34C25 39A10 47J15)",
 mrnumber      = "2379484 (2009e:37044)",
 zblnumber     = "1160.37016",
 doi           = "10.3934/dcds.2008.20.989",
 url           = "https://www.aimsciences.org/article/doi/10.3934/dcds.2008.20.989",
 language      = "english",
 annote        = "We consider discrete time systems
                  $x_{k+1}=U(x_{k};\lambda)$, $x\in R^{N}$, with a complex
                  parameter $\lambda$, and study their trajectories of large
                  amplitudes. The expansion of the map at infinity contains a
                  principal linear term, a bounded positively homogeneous
                  nonlinearity, and a smaller vanishing part. We study Arnold
                  tongues: the sets of parameter values for which the
                  large-amplitude periodic trajectories exist. The Arnold
                  tongues in problems at infinity generically are thick
                  triangles [4]; here we obtain asymptotic estimates for the
                  length of the Arnold tongues and for the length of their
                  triangular part. These estimates allow us to study
                  subfurcation at infinity. In the related problems on
                  small-amplitude periodic orbits near an equilibrium,
                  similarly defined Arnold tongues have the form of narrow
                  beaks. For standard pictures associated with the
                  Neimark-Sacker bifurcation of smooth discrete time systems
                  at an equilibrium, the Arnold tongues have asymptotically
                  zero width except for the strong resonance points. The
                  different shape of the tongues in the problem at infinity
                  is due to the non-polynomial form of the principal
                  homogeneous nonlinear term of the map $U(\cdot;\lambda)$:
                  this form implies non-degeneracy of the nonlinear terms in
                  the expansion of the map iterations and non-degeneracy of
                  the corresponding resonance functions.",
}

@MISC{KozCalPok:ArXiv10,
 author        = "Kozyakin, Victor and O'Callaghan, Brian and Pokrovskii,
                  Alexei",
 title         = "Sequences of Arbitrages",
 howpublished  = "ArXiv.org e-Print archive",
 year          = "2010",
 month         = apr,
 eprinttype    = "arXiv",
 eprint        = "1004.0561",
 doi           = "10.48550/arXiv.1004.0561",
 language      = "english",
 annote        = "The goal of this article is to understand some interesting
                  features of sequences of arbitrage operations, which look
                  relevant to various processes in Economics and Finances. In
                  the second part of the paper, analysis of sequences of
                  arbitrages is reformulated in the linear algebra terms.
                  This admits an elegant geometric interpretation of the
                  problems under consideration linked to the asynchronous
                  systems theory. We feel that this interpretation will be
                  useful in understanding more complicated, and more
                  realistic, mathematical models in economics.",
}

@ARTICLE{KozKraRa:DCDSS08,
 author        = "Kozyakin, Victor S. and Krasnosel'skii, Alexander M. and
                  Rachinskii, Dmitrii I.",
 title         = "Arnold tongues for bifurcation from infinity",
 journal       = "Discrete Contin. Dyn. Syst. Ser. S",
 fjournal      = "Discrete and Continuous Dynamical Systems. Series S",
 year          = "2008",
 volume        = "1",
 number        = "1",
 pages         = "107--116",
 issn          = "1937-1632",
 mrclass       = "39A11 (34B15 34C25 37G10 39A12)",
 mrnumber      = "2375587 (2008m:39010)",
 mrreviewer    = "Maria Patrizia Pera",
 zblnumber     = "1152.39006",
 doi           = "10.3934/dcdss.2008.1.107",
 language      = "english",
 annote        = "We consider discrete time systems
                  $x_{k+1}=U(x_{k};\lambda)$, $x\in\mathbf{R}^{N}$, with a
                  complex parameter $\lambda$. The map $U(\cdot;\lambda)$ at
                  infinity contains a principal linear term, a bounded
                  positively homogeneous nonlinearity, and a smaller part. We
                  describe the sets of parameter values for which the
                  large-amplitude $n$-periodic trajectories exist for a fixed
                  $n$. In the related problems on small periodic orbits near
                  zero, similarly defined parameter sets, known as Arnold
                  tongues, are more narrow.",
}

@ARTICLE{KKR:IFAC11,
 author        = "Kozyakin, Victor S. and Kuznetsov, Nikolay A. and Ryabykh,
                  Nikolay G.",
 title         = "A Pre-Encoding--Post-Decoding Technique for Stabilizing
                  Asynchronously Operating Systems",
 journal       = "IFAC Proceedings Volumes",
 year          = "2011",
 volume        = "44",
 number        = "1",
 pages         = "5855--5859",
 keywords      = "asynchronous systems; stability; convergence analysis",
 issn          = "1474-6670",
 doi           = "10.3182/20110828-6-IT-1002.00461",
 url           = "https://www.sciencedirect.com/science/article/pii/S1474667016445416",
 language      = "english",
 note          = "18th IFAC World Congress",
 annote        = "In the paper, a new method allowing to `asynchronously
                  stabilize' a broad class of control systems is developed.
                  Viability of the proposed approach is demonstrated by
                  examples among which an application to stabilizing unmanned
                  aerial vehicle systems. Pros and cons of the proposed
                  approach are discussed.",
}

@INPROCEEDINGS{KKKP:Rousse81:e,
 author        = "Krasnosel'skij, M. A. and Kozyakin, V. S. and
                  Krasnosel'skij, A. M. and Pokrovskij, A. V.",
 editor        = "Dimovski, I. and Stojanov, J.",
 title         = "On dynamics of control systems with several nonlinearities",
 booktitle     = "Proceedings of the Second Conference on Differential
                  Equations and Applications, Rousse, Bulgaria, June 29 --
                  July 4, 1981",
 organization  = "Technical University -- Rousse, Center of Mathematics",
 address       = "Rousse, Bulgaria",
 year          = "1982",
 volume        = "I",
 pages         = "366--376",
 zblnumber     = "0548.93038",
 language      = "english",
}

@ARTICLE{KKP:DAN96:e,
 author        = "Kuznetsov, N. A. and Kozyakin, V. S. and Pokrovskij, A. V.",
 title         = "A phenomenological model of the statistics of cycle lengths
                  and the first recurrence moments in discretizations of
                  dynamic systems",
 journal       = "Dokl. Math.",
 fjournal      = "Doklady Mathematics",
 year          = "1996",
 volume        = "54",
 number        = "1",
 pages         = "524--527",
 issn          = "1064-5624",
 mrclass       = "58F08 (58F03 58F13)",
 mrnumber      = "1440990 (98d:58095)",
 mrreviewer    = "Alexander Loskutov",
 zblnumber     = "0893.65052",
 language      = "english",
}

@INPROCEEDINGS{SBKK:CDC97,
 author        = "Su, Y.-F. and Bhaya, A. and Kaszkurewicz, E. and Kozyakin,
                  V. S.",
 title         = "Further results on stability of asynchronous discrete-time
                  linear systems",
 booktitle     = "Proc. 36th IEEE Conf. Decision and Control",
 year          = "1997",
 volume        = "1",
 pages         = "915--920",
 doi           = "10.1109/CDC.1997.650759",
 url           = "https://ieeexplore.ieee.org/document/650759",
 language      = "english",
 annote        = "Focuses on the stability problem of discrete-time
                  asynchronous linear systems, which can be viewed as linear
                  systems with time-varying delays. Within this context, a
                  stronger version of the necessity part of the classical
                  Chazan-Miranker theorem is proved and new results for
                  special classes of system matrices are also presented.",
}

@ARTICLE{SBKK:LAA98,
 author        = "Su, Yangfeng and Bhaya, Amit and Kaszkurewicz, Eugenius and
                  Kozyakin, Victor S.",
 title         = "Further results on convergence of asynchronous linear
                  iterations",
 journal       = "Linear Algebra Appl.",
 fjournal      = "Linear Algebra and its Applications",
 year          = "1998",
 volume        = "281",
 number        = "1-3",
 pages         = "11--24",
 coden         = "LAAPAW",
 issn          = "0024-3795",
 mrclass       = "65F30 (65F10)",
 mrnumber      = "1645319 (99h:65087)",
 mrreviewer    = "W. Govaerts",
 zblnumber     = "0935.65021",
 doi           = "10.1016/S0024-3795(98)10030-7",
 url           = "https://www.sciencedirect.com/science/article/pii/S0024379598100307",
 language      = "english",
 annote        = "This paper focuses on the convergence problem of
                  asynchronous linear iterations. A stronger version of the
                  necessity part of the theorem of D.~Chazan and W.~Miranker
                  [ibid. 2, 199-222 (1969)] is proved and new results for
                  special classes of iteration matrices are also presented.",
}

@ARTICLE{VKKKLP:DAN81:e,
 author        = "Vladimirov, A. A. and Klepcyn, A. F. and Kozjakin, V. S. and
                  Krasnosel'skii, M. A. and Livshitz, E. A. and Pokrovskii,
                  A. V.",
 title         = "Vector hysteresis nonlinearities of the von {M}ises-{T}resca
                  type",
 journal       = "Sov. Phys., Dokl.",
 fjournal      = "Soviet Physics. Doklady",
 year          = "1981",
 volume        = "26",
 number        = "3",
 pages         = "506--509",
 issn          = "0038-5689",
 mrclass       = "73E05 (34G20)",
 mrnumber      = "616210 (82h:73035)",
 mrreviewer    = "Petr Proch{\'a}zka",
 language      = "english",
}

@ARTICLE{VKKM:DAN93:e,
 author        = "Vladimirov, A. A. and Kozyakin, V. S. and Kuznetsov, N. A.
                  and Mandel'baum, A.",
 title         = "An investigation of the dynamic complementarity problem by
                  methods of the theory of desynchronized systems",
 journal       = "Russ. Acad. Sci., Dokl., Math.",
 fjournal      = "Russian Academy of Sciences. Doklady. Mathematics",
 year          = "1993",
 volume        = "47",
 number        = "2",
 pages         = "169--173",
 issn          = "1064-5624",
 mrclass       = "93C10 (49J40 90C33)",
 mrnumber      = "1230078 (94c:93054)",
 zblnumber     = "0819.93065",
 zblreviewer   = "C. V{\^a}rsan (Bucure{\c{s}}ti)",
 language      = "english",
 annote        = "The so-called Skorokhod problem of processes with oblique
                  reflection appears as the dynamic complementarity problem
                  and methods of the theory of stability of desynchronized
                  systems are used to get unique solvability. The output of
                  the system is constrained to a closed convex set and the
                  motion on the boundary is determined by a special law of
                  reflection. Here, conditions on the generalized normal
                  vector are studied to guarantee the unique determination of
                  the output from the given input.",
}

@ARTICLE{Koz:AiT98:2:r,
 author        = "Асарин, Е. А. and Бахтин, И. А. and Бобылев, Н. А. and
                  Бондаренко, В. А. and Бурд, В. Ш. and Горин, Е. А. and
                  Емельянов, С. В. and Забрейко, П. П. and Иванов, Л. А. and
                  Козякин, В. С. and Красносельский, А. М. and Кузнецов, Н.
                  А. and Куржанский, А. Б. and Левин, А. Ю. and Мухамадиев,
                  Э. М. and Перов, А. И. and Покорный, Ю. В. and Покровский,
                  А. В. and Рачинский, Д. И. and Стрыгин, В. В. and Цыпкин,
                  Я. З. and Черноруцкий, В. В.",
 title         = "Памяти {М}.{А}. {К}расносельского",
 journal       = "Автом. и телемех.",
 fjournal      = "Автоматика и телемеханика",
 year          = "1998",
 number        = "2",
 pages         = "179--184",
 url           = "https://mi.mathnet.ru/at2436",
 language      = "russian",
}

@TECHREPORT{ABRMP92,
 author        = "Асарин, Е. А. and Владимиров, А. А. and Козякин, В. С. and
                  Мандельбаум, А. and Покровский, А. В.",
 title         = "Использование методов теории рассинхронизации при
                  исследовании динамики информационных сетей",
 institution   = "Институт проблем передачи информации, РАН",
 address       = "Москва",
 year          = "1992",
 number        = "Глава 1 отчета ``Перспективные средства телекоммуникаций и
                  интегрированные системы связи''",
 type          = "Проект ``Разработка методов синтеза интегрированных
                  коммуникационных систем''.",
 doi           = "10.13140/RG.2.2.13486.31046",
 language      = "russian",
 annote        = "Среди математических моделей, используемых для описания
                  функционирования информационных и вычислительных сетей,
                  важное место занимают детерминированные и стохастические
                  модели сетей с непрерывными потоками и очередями
                  (гидродинамические модели). Во многих ситуациях
                  математическое описание динамики таких моделей приводит к
                  так называемой задаче Скорохода или динамической задаче
                  дополнительности на ортанте в конечномерном евклидовом
                  пространстве.\par В первой части главы для математического
                  исследования динамической задачи дополнительности
                  используются уже достаточно хорошо развитые методы теории
                  рассинхронизованных систем. С помощью этих методов удается
                  получить ряд новых результатов, в частности, новый критерий
                  однозначной разрешимости динамической задачи
                  дополнительности.\par Во второй половине главы исследуются
                  так называемые линейные модели сетей с фазово-частотной
                  рассинхронизацией. Такие модели позволяют решать задачи
                  анализа и синтеза сетей, в нескольких узлах которых
                  периодически (но в общем случае с разными периодами) и
                  независимо происходят изменения маршрутизации. Выясняется
                  роль синхронности и асинхронности при работе таких сетей.
                  Показывается, что зачастую можно обойтись без синхронизации
                  узлов. Дается детальное описание асимптотического поведения
                  сетей указанного типа.\par Первая часть главы (динамическая
                  задача дополнительности) написана А.~А.~Владимировым,
                  В.~С.~Козякиным и А.~Мандельбаумом (Израиль). Вторая часть
                  (фазово-частотная рассинхронизация) написана Е.~А.~Асариным
                  и А.~В.~Покровским.",
}

@BOOK{AKKK:92:r,
 author        = "Асарин, Е. А. and Козякин, В. С. and Красносельский, М. А.
                  and Кузнецов, Н. А.",
 title         = "Анализ устойчивости рассинхронизованных дискретных систем",
 publisher     = "Наука",
 address       = "М.",
 year          = "1992",
 pagetotal     = "408",
 isbn          = "5-02-006946-9",
 doi           = "10.13140/RG.2.1.3381.6169",
 url           = "http://eqworld.ipmnet.ru/ru/library/books/AsarinKozyakinKrasnoselskijKuznecov1992ru.pdf",
 language      = "russian",
 annote        = "Монография посвящена математическим методам изучения влияния
                  рассинхронизации обмена данными между отдельными
                  подсистемами на динамику системы в целом. Теория
                  рассинхронизованных систем находится в стадии формирования;
                  многие принципиальные вопросы, простые в случае
                  синхронизованных систем, для рассинхронизованных систем
                  либо открыты до сих пор, либо для своего решения требуют
                  развития специальной техники. Предлагается систематическое
                  изложение теории устойчивости рассинхронизованных систем в
                  различных классах рассинхронизаций. Часть результатов
                  относится к линейным системам, представляя собой новую
                  главу теории матриц, в которой изучаются свойства
                  бесконечных произведений так называемых помесей матриц.
                  Значительное внимание уделено анализу корректности
                  предлагаемых моделей. Книга содержит большое число примеров
                  и постановок открытых вопросов.\par Для инженеров,
                  математиков, специалистов по теории управления и системному
                  анализу.",
}

@INBOOK{AKKK:94:r,
 author        = "Асарин, Е. А. and Козякин, В. С. and Красносельский, М. А.
                  and Кузнецов, Н. А.",
 title         = "Математические модели устойчивости рассинхронизованных
                  систем",
 booktitle     = "Интеллектуальные процессы и их моделирование. Информационные
                  сети",
 publisher     = "Изд-во РАН",
 address       = "М.",
 year          = "1994",
 pages         = "3--17",
 language      = "russian",
 annote        = "Рассматриваются многокомпонентные системы, компоненты
                  которых подвергаются коррекции в дискретные моменты
                  времени. Предполагается, что в общем случае моменты
                  коррекции различных компонент не совпадают друг с другом.
                  Такие системы называются рассинхронизованными. Типичным
                  примером являются многопроцессорные системы и
                  вычислительные системы с асинхронной организацией
                  вычислений. Возникающие при описании динамики таких систем
                  разностные уравнения описывают также поведение цифровых
                  сетей интегрального обслуживания (телефон, радиовещание,
                  телевидение, передача данных). Аналогичными уравнениями
                  описывается функционирование многоконтурных систем
                  управления динамическими объектами, т.е. систем управления
                  технологическими процессами и движущимися объектами. Авторы
                  надеются, что подобные математические модели окажутся
                  полезными при исследовании информационного взаимодействия в
                  живых организмах и для описания нейроподобных сетей.\par В
                  статье исследуется вопрос о влиянии моментов коррекции
                  компонент на устойчивость системы. Анализируются три
                  принципиально различающиеся как по методам исследования.
                  так и по получающимся результатам ситуации. Первая из них
                  имеет дело со случаем, когда компоненты системы
                  подвергаются коррекции периодически с несовпадающими,
                  вообще говоря, периодами. Вторая ситуация относится к
                  случаю, когда моменты коррекции каждой компоненты
                  представляют взаимно независимые потоки случайных событий.
                  Третья ситуация относится к случаю, когда никакой
                  информацией о закономерностях, описывающих моменты
                  коррекции компонент, мы не располагаем. Полученные
                  результаты показывают, что способ рассинхронизации может
                  качественно влиять на динамику системы. В ряде случаев
                  рассинхронизованные системы обладают свойствами, которыми
                  не обладают синхронизованные системы.",
}

@ARTICLE{AKKS:DU74:r,
 author        = "Ахмеров, Р. Р. and Каменский, М. И. and Козякин, В. С. and
                  Соболев, А. В.",
 title         = "Периодические решения систем автономных
                  функционально-дифференциальных уравнений нейтрального типа
                  с малым запаздыванием",
 journal       = "Дифференц. уравнения",
 fjournal      = "Дифференциальные уравнения",
 year          = "1974",
 volume        = "10",
 number        = "11",
 pages         = "1923--1931",
 url           = "https://mi.mathnet.ru/de2304",
 language      = "russian",
 annote        = "В статье доказана теорема существования периодических
                  решений систем автономных функционально-дифференциальных
                  уравнений нейтрального тина с малым отклонением аргумента
                  следующего вида: \[ z'(t)=f(V(t,\varepsilon, z),
                  V(t,\varepsilon, z'), \varepsilon),\tag{$*$} \] где
                  оператор $f$ действует из $C( [-h, h], R^{n})\times
                  C([-h,h],R^{n}) \times [0, 1]$ в $R^{n}$, $z$ ---
                  неизвестная функция; оператор $V$ действует из $R^{1}\times
                  [0, 1]\times C(( -\infty,\infty), R^{n})$ в $C([-h,h],
                  R^{n})$ и определяется формулой \[ [V(t, \varepsilon, z) ]
                  (s) = z(t +\varepsilon s),\qquad s\in[-h, h]; \]
                  $\varepsilon\in[0, 1]$ --- малый параметр, характеризующий
                  отклонение аргумента. Параметр $\varepsilon$ действительно
                  характеризует величину отклонения аргумента, так как при
                  фиксированном $\varepsilon$ значение производной решения
                  уравнения $(*)$ в точке $t$ определяется поведением решения
                  и его производной на отрезке $[t-\varepsilon h,
                  t+\varepsilon h]$. При $\varepsilon= 0$ уравнение $(*)$
                  превращается, как нетрудно видеть, в обыкновенное
                  дифференциальное уравнение \[
                  z'(t)=f(\overline{z(t)},\overline{z'(t)}, 0).\tag{$**$} \]
                  Здесь $\overline{z(t)}$ и $\overline{z'(t)}$ в правой части
                  уравнения $(**)$ обозначают функции-константы из $C([-h,
                  h], R^{n})$: $[\overline{z(t)}](s) = [V(t,0,z)](s)\equiv
                  z(t)$, $[\overline{z'(t)}](s) \equiv z'(t)$.",
}

@ARTICLE{ECG:80:r,
 author        = "Бланк, М. Л. and Гуковский, Д. Э. and Давиденко, А. В. and
                  Козякин, В. С. and Красносельский, А. М. and Марковская, Т.
                  С. and Меркулова, И. Н. and Руда, М. Я. and Соболев, А.
                  В.",
 title         = "Экспериментальная система автоматического анализа сердечного
                  ритма",
 journal       = "Бюллетень ВКНЦ АМН СССР",
 year          = "1980",
 volume        = "2",
 pages         = "81--84",
 language      = "russian",
 annote        = "В настоящей работе представлены данные об экспериментальном
                  варианте системы автоматического анализа аритмий,
                  предназначенной для слежения за ритмом сердца (по
                  мониторному отведению ЭКГ в палате интенсивного наблюдения)
                  в режиме реального времени. Данная система позволяет
                  накапливать и хранить информацию о ритме сердца и его
                  нарушениях и выдавать ее по требованию врача на экран или
                  печатающее устройство в виде графиков, и таблиц. Эта
                  система является комплексом программ, работающих в
                  мультипрограммном режиме, написанных на алгоритмических
                  языках HP-ASSEMB-LER и FORTRAN. Связи между программами
                  осуществляются посредством двух циклических буферов. Первый
                  из них содержит электрокардиосигнал (ЭКС) за последние 10
                  сек. наблюдения, дискретизированный с частотой 200 Гц, а во
                  втором находятся измеряемые системой параметры последних
                  128 кардиоциклов. Система реализована на мини-ЭВМ фирмы
                  ``Хьюлетт-Паккард'' HP 2100А (советские аналоги М-6000 и
                  СМ-1) с аналогоцифровым преобразователем, внешним
                  запоминающим устройством (диском), дисплеем HP 2640С и
                  алфавитно-цифровым печатающим устройством.\par Система
                  позволяет получать следующие виды информации: а) информацию
                  об основном ритме сердца (синусовом ритме, мерцательной
                  аритмии, узловом ритме, синусовой аритмии); б) информацию
                  об отдельных видах аритмий на фоне основного ритма
                  (желудочковых экстрасистолах различных видов, коротких, из
                  трех или более комплексов пароксизмах желудочковой
                  тахикардии, единичных или групповых наджелудочковых
                  экстрасистолах, коротких пароксизмах наджелудочковой
                  тахикардии, отдельных блокированных предсердных комплексах,
                  группах блокированных предсердных комплексов, ускользающих
                  сокращениях).",
}

@TECHREPORT{ECG:82:2,
 author        = "Бланк, М. Л. and Гуковский, Д. Э. and Давиденко, А. В. and
                  Козякин, В. С. and Красносельский, А. М. and Марковская, Т.
                  С. and Меркулова, И. Н. and Руда, М. Я. and Соболев, А.
                  В.",
 title         = "Разработка системы автоматической диагностики нарушений
                  ритма сердца в реальном масштабе времени",
 institution   = "ВНТИЦентр",
 address       = "М.",
 year          = "1985",
 number        = "81024272",
 pagetotal     = "123",
 type          = "Отчет ВКНЦ АМН СССР",
 language      = "russian",
}

@BOOK{MTS:86:r,
 author        = "Бобылев, Н. А. and Болтянский, В. Г. and Всехсвятский, С. Ю.
                  and Калашников, В. В. and Козякин, В. С. and Колмановский,
                  В. Б. and Красносельский, А. М. and Покровский, А. В.",
 title         = "Математическая теория систем",
 publisher     = "Наука",
 address       = "М.",
 year          = "1986",
 pagetotal     = "166",
 doi           = "10.13140/RG.2.1.4430.1924",
 language      = "russian",
 annote        = "В книге изложен ряд разделов современной математической
                  теории систем. Рассмотрены методы решения оптимизапионных
                  задач для различных классов систем. Большое внимание
                  уделено методам исследования динамики процессов в общих
                  нелинейных системах и системах с нестандартными звеньями;
                  изучены способы приближенного построения решений и
                  возможности упрощения соответствующих уравнений;
                  исследованы свойства стохастических моделей.\par Для
                  специалистов по теории систем, теории управления,
                  математиков, механиков.",
}

@ARTICLE{VKKKLP:DAN81:r,
 author        = "Владимиров, А. А. and Клепцын, А. Ф. and Козякин, В. С. and
                  Красносельский, М. А. and Лифшиц, Е. А. and Покровский, А.
                  В.",
 title         = "Векторные гистерезисные нелинейности типа
                  {М}изеса--{Т}реска",
 journal       = "Докл. АН СССР",
 fjournal      = "Доклады АН СССР",
 year          = "1981",
 volume        = "257",
 number        = "3",
 pages         = "581--584",
 url           = "https://mi.mathnet.ru/dan44335",
 language      = "russian",
}

@ARTICLE{VKKM:DAN93:r,
 author        = "Владимиров, А. А. and Козякин, В. С. and Кузнецов, Н. А. and
                  Мандельбаум, А.",
 title         = "Об исследовании динамической задачи дополнительности
                  методами теории рассинхронизованных систем",
 journal       = "Докл. АН СССР",
 fjournal      = "Доклады АН СССР",
 year          = "1993",
 volume        = "329",
 number        = "1",
 pages         = "5--8",
 url           = "https://mi.mathnet.ru/dan5259",
 language      = "russian",
 annote        = "Методы теории устойчивости рассинхронизованных систем
                  используются для получения условий однозначной разрешимости
                  динамической задачи дополнительности, являющейся частным
                  случаем так называемой задачи Скорохода или задачи о
                  процессах с косым отражением.",
}

@INCOLLECTION{VKP:PMFA85:r,
 author        = "Владимиров, А. А. and Козякин, В. С. and Покровский, А. В.",
 title         = "Абсолютная диссипативность систем с гистерезисом",
 booktitle     = "Прикладные методы функционального анализа. Межвузовский
                  сб.",
 publisher     = "ВГУ",
 address       = "Воронеж",
 year          = "1985",
 pages         = "33--40",
 language      = "russian",
}

@ARTICLE{VGKKPR:INFOPROC11-2:r,
 author        = "Владимиров, А. Г. and Гречишкина, Н. А. and Козякин, В. С.
                  and Кузнецов, Н. А. and Покровский, А. В. and Рачинский, Д.
                  И.",
 title         = "Асинхронность: теория и практика",
 journal       = "Информационные процессы",
 year          = "2011",
 volume        = "11",
 number        = "1",
 pages         = "1--45",
 url           = "http://www.jip.ru/2011/1-45-2011.pdf",
 language      = "russian",
 annote        = "Дается обзор результатов последнего времени, связанных с
                  теоретическим анализом идеи ``асинхронности'' и ее
                  применением в некоторых прикладных задачах.\par Первая
                  часть работы посвящена описанию новых качественных и
                  численных методов оценки совместного спектрального радиуса
                  семейств матриц. Приводятся эффективные оценки скорости
                  приближения спектрального радиуса матрицы с помощью формулы
                  Гельфанда. Полученные результаты распространяются на случай
                  вычисления совместного спектрального радиуса для семейств
                  матриц. Значительное внимание уделено описанию алгоритмов
                  приближенного построения норм Барабанова и вычисления
                  совместного спектрального радиуса семейства матриц с любой
                  наперед заданной точностью, позволяющие оценить
                  апостериорную погрешность вычисления совместного
                  спектрального радиуса.\par Во второй части работы
                  приводятся примеры применения идеи асинхронности для
                  анализа нелинейной динамики лазеров с очень большим или
                  бесконечным числом степеней свободы. Описаны процессы,
                  приводящие к самоорганизации процессов синхронизации
                  различных элементов системы. Основное внимание уделяется
                  малоизученным бифуркационным механизмам возникновения и
                  нарушения синхронизации и сопутствующих ей режимов. Здесь
                  же приводится описание математических моделей
                  рассинхронизованных сетей состоящие из элементов с памятью.
                  Этот класс математических моделей имеет значительный
                  потенциал для адекватного описания различных процессов в
                  экономике, биологии, технике и т.д. Продемонстрирована роль
                  предложенного класса моделей в контексте понимания
                  долговременных последствий экономических кризисов. Описаны
                  эффективные методы их качественного и численного
                  исследования для этого класса моделей.",
}

@ARTICLE{DK:INFOPROC11:r,
 author        = "Дай, C. and Козякин, В. С.",
 title         = "Конечная достижимость обобщенного спектрального радиуса
                  ограниченного множества матриц с равномерно субпериферийным
                  спектром",
 journal       = "Информационные процессы",
 year          = "2011",
 volume        = "11",
 number        = "2",
 pages         = "253--261",
 url           = "http://www.jip.ru/2011/253-261-2011.pdf",
 language      = "russian",
 annote        = "В статье предлагаются условия, гарантирующие конечную
                  достижимость обобщенного спектрального радиуса
                  ограниченного множества $\boldsymbol{S}=\{S_k\}_{k\in K}$
                  вещественных или комплексных матриц. Доказано, что
                  существование последовательности матричных произведений
                  $\boldsymbol{S}_{{\sigma(n_{\ell})}}$ длины
                  $n_{\ell}\to\infty$ с сомножителями из $\boldsymbol{S}$,
                  обладающих тем свойством, что спектр каждой матрицы
                  $\boldsymbol{S}_{{\sigma(n_{\ell})}}$ равномерно
                  субпериферийный и \[
                  {\rho}({\boldsymbol{S}}):=\sup_{n\ge1}\sup_{i_1,\dotsc,i_n\in
                  K}\sqrt[n]{{\rho(S_{i_1}\dotsm
                  S_{i_n})}}=\lim_{\ell\to+\infty}
                  \sqrt[\uproot{3}n_{\ell}]{\rho(\boldsymbol{S}_{\!{\sigma(n_{\ell})}})},
                  \] влечет конечную достижимость обобщенного спектрального
                  радиуса $\boldsymbol{S}$.",
}

@ARTICLE{DKKKP:DAN95:r,
 author        = "Даймонд, Ф. and Клоеден, П. and Козякин, В. С. and
                  Красносельский, М. А. and Покровский, А. В.",
 title         = "Грубость траекторий динамических систем по отношению к
                  гистерезисным возмущениям",
 journal       = "Докл. РАН",
 fjournal      = "Доклады РАН",
 year          = "1995",
 volume        = "343",
 number        = "1",
 pages         = "25--27",
 url           = "https://mi.mathnet.ru/dan4417",
 language      = "russian",
 annote        = "Рассмотрим гладкое отображение $f:\Re^{d}\to\Re^{d}$.
                  Системы вида \[ x_{n}=f(x_{n-1})\tag{$*$}\] являются
                  классическим средством описания динамики систем управления,
                  объектов технического, механического и др. происхождения.
                  Обычно уравнения ($*$) описывают динамику соответствующих
                  реальных систем лишь приближенно, и возникает проблема их
                  грубости по отношению к возмущениям различной природы.
                  Согласно классическим результатам, достаточно гладкие
                  системы ($*$) сохраняют многие структурные свойства при
                  гладких (малых в метрике $C^{1}$) возмущениях. Имеются,
                  однако, классы негладких возмущений, представляющих
                  значительный интерес. К ним относятся прежде всего
                  различного рода аппроксимации и интерполяции, временные и
                  пространственные дискретизации и т.п. Для их анализа в
                  статье используется техника, недавно предложенная авторами
                  для приближенного исследования хаотических динамических
                  систем.",
}

@ARTICLE{DKKKP:AIT95:r,
 author        = "Даймонд, Ф. and Клоеден, П. and Козякин, В. С. and
                  Красносельский, М. А. and Покровский, А. В.",
 title         = "Периодические траектории негладких возмущений систем с
                  хаотическим поведением",
 journal       = "Автом. и телемех.",
 fjournal      = "Автоматика и телемеханика",
 year          = "1995",
 number        = "5",
 pages         = "34--41",
 url           = "https://mi.mathnet.ru/at3640",
 language      = "russian",
 annote        = "В статье проводится анализ периодических режимов систем со
                  сложным псевдохаотическим поведением при малых негладких их
                  возмущениях. Предполагается, что исходная система обладает
                  свойством полугиперболичности, близким к традиционному
                  понятию гиперболичности.\par Недавно выяснено, что при
                  синтезе детерминированных систем управления полезно вводить
                  участки псевдохаотического (например, гиперболического)
                  поведения. Это позволяет в ряде случаев упростить алгоритмы
                  управления и добиться ряда других преимуществ. При этом
                  важны оценки влияния на основные глобальные характеристики
                  системы в зоне ее хаотического поведения малых шумов и
                  искажений характеристик звеньев системы. Некоторые
                  результаты в этом направлении получены для гладких
                  возмущений рассматриваемых систем. В то же время во многих
                  приложениях принципиальна именно негладкость возмущений
                  (негладкие возмущения типичны для систем управления,
                  негладкость блокирует применение хорошо разработанных
                  методов теории структурной устойчивости и т.д.). Изучаемая
                  в статье глобальная характеристика --- это структура
                  множества периодических режимов возмущенных систем.
                  Получение результатов в этом направлении --- основная тема
                  статьи.",
}

@ARTICLE{DKKP:AIT95-2:r,
 author        = "Даймонд, Ф. and Клоеден, П. and Козякин, В. С. and
                  Красносельский, М. А. and Покровский, А. В.",
 title         = "Робастность наблюдаемого поведения полугиперболических
                  динамических систем",
 journal       = "Автом. и телемех.",
 fjournal      = "Автоматика и телемеханика",
 year          = "1995",
 number        = "11",
 pages         = "148--159",
 url           = "https://mi.mathnet.ru/at3750",
 language      = "russian",
 annote        = "Понятие взаимного шедоуинга формализует представление о
                  грубости наблюдаемого поведения динамических систем и может
                  рассматриваться как ослабленная форма структурной
                  устойчивости, полезная при изучении динамики управляемых
                  систем. Взаимный шедоуинг включает в себя понятия шедоуинга
                  как истинных, так и псевдотраекторий динамической системы.
                  Показывается, что системы, порождаемые полугиперболическими
                  липшицевыми отображениями, не являющимися в общем случае ни
                  гладкими, ни обратимыми, обладают свойством взаимного
                  шедоуинга.",
}

@ARTICLE{KKKK:AiT83:7:r,
 author        = "Клепцын, А. Ф. and Козякин, В. С. and Красносельский, М. А.
                  and Кузнецов, Н. А.",
 title         = "О влиянии малой рассинхронизации на устойчивость сложных
                  систем. {I}",
 journal       = "Автом. и телемех.",
 fjournal      = "Автоматика и телемеханика",
 year          = "1983",
 number        = "7",
 pages         = "44--51",
 url           = "https://mi.mathnet.ru/at5171",
 language      = "russian",
 annote        = "Изучаются эффекты, связанные с малыми рассогласованиями по
                  фазе в системах с дискретными элементами. \par Исследование
                  динамики сложных систем управления, содержащих одновременно
                  звенья непрерывного действия и различные звенья импульсного
                  типа (экстраполяторы, ключи, элементы памяти, ЦВМ и др.),
                  обычно пытаются свести к анализу либо дифференциальных,
                  либо разностных уравнений. При построении разностных
                  уравнений часто не учитывается неизбежная малая
                  рассинхронизация моментов включения импульсных элементов;
                  это приводит к неверным выводам. Авторам довелось
                  участвовать в обсуждении возникающих здесь ситуаций, в
                  выяснении причин неверных выводов, в разработке приемов
                  анализа. В ряде случаев можно обойтись классическими
                  конструкциями, в других нужны новые простые построения.
                  Некоторые из них излагаются в статье.",
}

@ARTICLE{KKKK:AiT84:3:r,
 author        = "Клепцын, А. Ф. and Козякин, В. С. and Красносельский, М. А.
                  and Кузнецов, Н. А.",
 title         = "О влиянии малой рассинхронизации на устойчивость сложных
                  систем. {II}",
 journal       = "Автом. и телемех.",
 fjournal      = "Автоматика и телемеханика",
 year          = "1984",
 number        = "3",
 pages         = "42--47",
 url           = "https://mi.mathnet.ru/at4638",
 language      = "russian",
 annote        = "Продолжение работы~\cite{KKKK:AiT83:7:r}. Описываются классы
                  нечувствительных к рассинхронизации линейных систем с
                  дискретными элементами.",
}

@ARTICLE{KKKK:AiT84:8:r,
 author        = "Клепцын, А. Ф. and Козякин, В. С. and Красносельский, М. А.
                  and Кузнецов, Н. А.",
 title         = "О влиянии малой рассинхронизации на устойчивость сложных
                  систем. {III}",
 journal       = "Автом. и телемех.",
 fjournal      = "Автоматика и телемеханика",
 year          = "1984",
 number        = "8",
 pages         = "63--67",
 url           = "https://mi.mathnet.ru/at4795",
 language      = "russian",
 annote        = "Продолжение работ~\cite{KKKK:AiT83:7:r,KKKK:AiT84:3:r}.
                  Изучаются эффекты, связанные с рассинхронизацией по частоте
                  в системах с дискретными элементами.",
}

@ARTICLE{KKKK:DAN84:r,
 author        = "Клепцын, А. Ф. and Козякин, В. С. and Красносельский, М. А.
                  and Кузнецов, Н. А.",
 title         = "Устойчивость рассинхронизованных систем",
 journal       = "Докл. АН СССР",
 fjournal      = "Доклады АН СССР",
 year          = "1984",
 volume        = "274",
 number        = "5",
 pages         = "1053--1056",
 url           = "https://mi.mathnet.ru/dan46463",
 language      = "russian",
 annote        = "Изучаются системы $W$, динамика которых в непрерывном
                  времени, описывается уравнениями,
                  \[x_{i}(T_{i}^{n+1})=\sum_{j=1}^{N}
                  a_{ij}x_{j}(T_{j}^{n})\tag{$*$} \] Каждая переменная
                  $x_{i}$ либо скалярная, либо векторная некоторой
                  размерности $d^j$. Предполагается, что функция $x_{i}(t)$
                  на каждом промежутке $T^{n} < t\le T_{i}^{n+1}$ изменения
                  времени между моментами $T^{n}$ и $T_{i}^{n+1}$
                  переключений принимает постоянное значение. Символом
                  $a_{ij}$ в случае скалярных переменных обозначаются числа,
                  а в случае векторных переменных --- прямоугольные или
                  квадратные матрицы соответствующих порядков. Системы ($*$)
                  возникают в ситуациях, когда реализация переключений
                  отдельных переменных $x_{i}$ осуществляется независимо (в
                  результате использования независимо функционирующих
                  устройств; в результате рассинхро-низованно действующих
                  звеньев типа экстраполяторов, ключей, элементов памяти и
                  др.; при временных отключениях отдельных регуляторов и
                  т.д.).",
}

@ARTICLE{KozKraPok:DAN72:r,
 author        = "Козякин, B. C. and Красносельский, М. А. and Покровский, А.
                  В.",
 title         = "Виброустойчивые гистероны",
 journal       = "Докл. АН СССР",
 fjournal      = "Доклады АН СССР",
 year          = "1972",
 volume        = "206",
 number        = "4",
 pages         = "800--803",
 url           = "https://mi.mathnet.ru/dan37159",
 language      = "russian",
 annote        = "Рассматривается нелинейный преобразователь $W$, состояние
                  которого в каждый момент времени $t$ определяется парой
                  чисел $\{u, x\}$. Предполагается, что $W$ преобразует
                  каждую кусочно монотонную и непрерывную функцию $u(t)$,
                  заданную на некотором промежутке $[t_0, t_1]$, в
                  непрерывную функцию $x(t)$, которая зависит также от
                  состояния $\{u_0, x_0\}$ преобразователя $W$ в момент $t =
                  t_0$ (функция $u(t)$ должна при этом удовлетворять условию
                  $u(t_0) = u_0$). Соответствие между $u(t)$ и $x(t)$ будем
                  описывать равенством $x(t) = W[t_0,x_0]u(t)$. Функцию
                  $u(t)$ будем называть управлением, а функцию $x(t)$
                  выходным сигналом. Физическая природа преобразователя $W$
                  для нас не важна; если $W$ --- одномерный пластический
                  элемент, то роль управления может играть переменная
                  деформация, а выходного сигнала --- внутреннее напряжение;
                  если $W$ --- намагничиваемый элемент, то роль управления
                  может играть переменная напряженность внешнего магнитного
                  поля, а выходного сигнала --- магнитная индукция. Для нас
                  преобразователь --- черный ящик. Преобразователь $W$
                  назовем гистероном, если он обладает полугрупповым
                  свойством: при любых \[
                  W[t_1,W[t_0,x_0]u(t_1)]u(t_2)=W[t_0,x_0]u(t_2).\] Изучаются
                  условия, при которых гистерон $W$ может быть продолжен по
                  непрерывности с множества кусочно-монотонных входов на
                  множество непрерывных входов.",
}

@ARTICLE{Koz:TrVGU70:r,
 author        = "Козякин, В. С.",
 title         = "Об уплотняющих и сжимающих операторах",
 journal       = "Труды математического факультета ВГУ",
 year          = "1970",
 number        = "1",
 pages         = "60--70",
 language      = "russian",
 annote        = "Понятия меры некомпактности и уплотняющих операторов
                  позволили получить ряд новых фактов в теории вращения
                  векторных полей и неподвижных точек. При некоторых условиях
                  свойства уплотняющих операторов оказываются аналогичными
                  свойствам сжимающих операторов. Попытка исследовать эту
                  взаимосвязь предпринимается в работе.",
}

@ARTICLE{Koz:MATZAME72:r,
 author        = "Козякин, В. С.",
 title         = "Об одном функциональном уравнении",
 journal       = "Матем. заметки",
 year          = "1971",
 volume        = "9",
 number        = "2",
 pages         = "161--170",
 url           = "https://mi.mathnet.ru/mz9655",
 language      = "russian",
 annote        = "Доказываются теоремы существования и находятся непрерывные,
                  определенные на всей вещественной оси $R$ решения
                  функционального уравнения $f(t)=A[t,f(at-b),f(at-c)]$, где
                  $a, b, c$ --- вещественные параметры, $A:R\times E\times
                  E\to E$ --- непрерывный оператор, $E$ --- банахово
                  пространство.",
}

@ARTICLE{Koz:UMN72:r,
 author        = "Козякин, В. С.",
 title         = "О виброустойчивости дифференциальных уравнений второго
                  порядка",
 journal       = "Успехи матем. наук",
 year          = "1972",
 volume        = "27",
 number        = "5",
 pages         = "241--242",
 url           = "https://mi.mathnet.ru/umn5121",
 language      = "russian",
 annote        = "В недавней работе М.~А.~Красносельского и А.~В.~Покровского
                  выделено и изучено новое понятие виброустойчивости
                  дифференциальных уравнений. Как оказалось, к исследованию
                  таких уравнений сводится математическое описание некоторых
                  моделей пластических тел. В работе М.~А.~Красносельского и
                  А.~В.~Покровского изучены лишь системы уравнений первого
                  порядка; в настоящей работе предлагается аналогичная теория
                  для дифференциальных уравнений второго порядка.",
}

@ARTICLE{Koz:TrVGU72:r,
 author        = "Козякин, В. С.",
 title         = "Об обратном неравенстве Минковского для монотонных функций",
 journal       = "Труды НИИ математики ВГУ",
 year          = "1972",
 number        = "5",
 pages         = "59--64",
 language      = "russian",
 annote        = "В работе Э.~Беккенбаха и Р.~Беллмана (Неравенства, М., Мир,
                  1965, стр.~60--65) изучен вопрос о том, для каких классов
                  функций $f,g\in L_p$ при некотором фиксированном
                  $\varkappa$ верно неравенство \[ \int fg\,dx \ge \varkappa
                  \left(\int f^{p}\,dx \right)^{\frac{1}{p}} \left(\int
                  g^{q}\,dx \right)^{\frac{1}{q}},\qquad
                  \frac{1}{p}+\frac{1}{q}=1, \] которое естественно назвать
                  обратным неравенством Гёльдера. В работе Э.~Беккенбаха и
                  Р.~Беллмана поводятся достатопные условия, при которых
                  выполняется это неравенство. Возникает аналогичный вопрос о
                  том, для каких классов функций выполнияется ``обратное
                  неравенство Минковского'': \[ \left(\int
                  |f+g|^{p}\,dx\right)^{\frac{1}{p}} \ge \varkappa
                  \left[\left(\int f^{p}\,dx \right)^{\frac{1}{p}}+
                  \left(\int g^{q}\,dx \right)^{\frac{1}{p}}\right],\qquad
                  p>1, \] Очевидно, последнее неравенство выполняется при
                  $\varkappa=2^{\frac{1-p}{p}}$, если функции $f$ и $g$
                  одного знака. Другой менее очевидный класс функций, для
                  которых справедливо это неравенство, изучен в работе
                  методами теории конусов.",
}

@INCOLLECTION{Koz:DE76-1:r,
 author        = "Козякин, В. С.",
 title         = "Второе необходимое условие бифуркации {$N$}-периодических
                  точек",
 booktitle     = "Дифференциальные уравнения. Межвузовский сб.",
 publisher     = "КГУ",
 address       = "Куйбышев",
 year          = "1976",
 pages         = "39--44",
 language      = "russian",
}

@INCOLLECTION{Koz:DE76-2:r,
 author        = "Козякин, В. С.",
 title         = "О разрушении инвариантных торов",
 booktitle     = "Дифференциальные уравнения. Межвузовский сб.",
 publisher     = "КГУ",
 address       = "Куйбышев",
 year          = "1976",
 pages         = "45--50",
 language      = "russian",
}

@ARTICLE{Koz:UMN77:r,
 author        = "Козякин, В. С.",
 title         = "О рождении периодических точек из положения равновесия",
 journal       = "Успехи матем. наук",
 year          = "1977",
 volume        = "32",
 number        = "4",
 pages         = "255--256",
 url           = "https://mi.mathnet.ru/umn3226",
 language      = "russian",
 annote        = "Обсуждается вопрос о рождении малых периодических точек
                  некоторого отображения $X(x,\varepsilon)$,
                  $X(0,\varepsilon)\equiv 0$. Изучается лишь отображение
                  плоскости, так как в широких предположениях $N$-мерный
                  случай ($N>2$) принципиально не отличается от двумерного.
                  Установлены условия рождения периодических точек из
                  положения равновесия отображения $X(x,\varepsilon)$,
                  периоды которых стремятся к бесконечности при
                  $\varepsilon\to 0$.",
}

@ARTICLE{Koz:DAN77:232:r,
 author        = "Козякин, В. С.",
 title         = "Субфуркация периодических колебаний",
 journal       = "Докл. АН СССР",
 fjournal      = "Доклады АН СССР",
 year          = "1977",
 volume        = "232",
 number        = "1",
 pages         = "25--27",
 url           = "https://mi.mathnet.ru/dan40846",
 language      = "russian",
}

@ARTICLE{Koz:SMZh77:r,
 author        = "Козякин, В. С.",
 title         = "Явление субфуркации при потере устойчивости положения
                  равновесия системы дифференциальных уравнений с
                  запаздыванием",
 journal       = "Сибирский матем. журнал",
 year          = "1977",
 volume        = "18",
 number        = "3",
 pages         = "580--594",
 url           = "https://mi.mathnet.ru/smj6198",
 language      = "russian",
 annote        = "Рассматривается зависящая от скалярного параметра $\lambda$
                  система дифференциальных уравнений с запаздывающим
                  аргументом \[\frac{dx}{dt}=f(\lambda,t,x_{t}).\] Здесь $x=
                  \{x_{1}, x_{2},\ldots,x_{n}\}$ --- точка пространства
                  $R^{n}$; символ $x_{t}$ обозначает непрерывную
                  вектор-функцию $x_{t}(s)=\{x_{1}(t+s),x_{2}(t+s),\ldots,
                  x_{n}(t+s)\}$ переменной $s\in [-h, 0]$ $(h\ge 0)$;
                  $f(\lambda,t,x_{t})$ --- $T$-периодический no $t$ оператор
                  $(T>0)$ со значениями в $R^{n}$, определенный по третьему
                  аргументу на множестве непрерывных на $[-h, 0]$ функций
                  достаточно малой равномерной нормы, $f(\lambda,t,0)\equiv
                  0$.\par В таком виде, например, может быть представлена
                  система дифференциальных уравнений с несколькими
                  дискретными запаздываниями или система с несколькими
                  распределенными запаздываниями, а также многие
                  дифференциальные уравнения с запаздывающим аргументом более
                  сложной природы.\par Пусть нулевое решение системы
                  устойчиво при $\lambda=\lambda_{1}$, но неустойчиво при
                  $\lambda=\lambda_{2}$ $(\lambda_{1}<\lambda_{2})$. Тогда
                  существует точка $\lambda=\lambda_{0}$ \emph{потери
                  устойчивости} нулевого решения системы, характеризующаяся
                  тем, что при $\lambda_{1}\le\lambda<\lambda_{0}$ нулевое
                  решение устойчиво, а как угодно близко справа от
                  $\lambda_{0}$ найдутся значения параметра, при которых
                  нулевое решение неустойчиво.\par В ряде задач важно знать,
                  каким образом происходит потеря устойчивости нулевого
                  решения системы. Это один из классических вопросов теорий
                  устойчивости движения. Ответам на этот вопрос при различных
                  ситуациях посвящена обширная литература. В работе изучается
                  новая ситуацию общего вида. Назовем $\lambda_{0}$
                  \emph{точкой субфуркации} периодических решений, если
                  система при некоторых $\lambda_{k}\to\lambda_{0}$ имеет
                  ненулевые периодические решения, амплитуды которых
                  стремятся к нулю при $k\to\infty$, а наименьшие периоды
                  которых неограниченно растут.\par Показывается, что в
                  достаточно широких предположениях относительно
                  $f(\lambda,t,x_{t})$ потеря устойчивости нулевого решения
                  ``почти всегда'' сопровождается субфуркацией. Результат нов
                  и для уравнений без запаздывания.",
}

@ARTICLE{Koz:NKZR82:r,
 author        = "Козякин, В. С.",
 title         = "О книге {Д}ж. {К}арра ``{П}рименения теории центрального
                  многообразия''",
 journal       = "Новые книги за рубежом",
 year          = "1982",
 volume        = "10",
 pages         = "16--19",
 language      = "russian",
}

@ARTICLE{Koz:AiT84:10:r,
 author        = "Козякин, В. С.",
 title         = "О пренебрежении малыми членами при исследовании нелинейных
                  систем",
 journal       = "Автом. и телемех.",
 fjournal      = "Автоматика и телемеханика",
 year          = "1984",
 number        = "10",
 pages         = "38--43",
 url           = "https://mi.mathnet.ru/at4854",
 language      = "russian",
 annote        = "Предлагается критерий, позволяющий судить о том, когда,
                  допустимо пренебрежение членами высших порядков малости в
                  задачах анализа нелинейных систем.\par Ряд задач теории
                  управления сводится к исследованию структуры множества
                  решений систем вещественных уравнений. Примером служит
                  задача об автоколебаниях динамической системы, описываемой
                  дифференциальными уравнениями. Здесь вопрос о существовании
                  периодических колебаний и их числе эквивалентен вопросу о
                  существовании и числе решений некоторой, вообще говоря,
                  зависящей от параметров
                  $\lambda_1,\lambda_2\ldots,\lambda_p$ системы вещественных
                  уравнений \[F_i(x_i, x_2,\ldots, x_m,
                  \lambda_1,\lambda_2\ldots,\lambda_p)=0\qquad (i=1,
                  2,\ldots,m).\tag{$*$}\] Часто при исследовании уравнений
                  ($*$) достаточно полная информация известна лишь о
                  нескольких первых членах разложения функции $F_i$ в ряд по
                  степеням $x_k$ и $\lambda_l$. Информация же об остальных
                  членах разложения носит, как правило, оценочный характер;
                  получение детальной информации об этих членах сопряжено с
                  большими трудностями, а нередко и вообще невозможно. В
                  связи с этим (и по многим другим причинам) важны схемы
                  исследования уравнений ($*$), в которых отбрасываются члены
                  достаточно большой степени разложения функций $F$, по
                  $x_{k}^{n}$ и $\lambda_{l}^{n}$ и вместо уравнений ($*$)
                  изучается получившаяся ``усеченная'' система алгебраических
                  уравнений. В одних случаях переход к усеченным уравнениям
                  позволяет сделать правильный вывод о строении множества
                  решений уравнений ($*$), в других случаях такой переход
                  приводит к ложным выводам. В каких же случаях при
                  исследовании уравнений допустимо их усечение? Этот вопрос
                  изучается в работе. Обсуждаемый вопрос родственен переходу
                  в задаче об устойчивости индивидуальных уравнений к
                  проблеме абсолютной устойчивости; анализу бифуркаций в
                  нелинейных задачах переходом к линеаризованным уравнениям,
                  и др.",
}

@ARTICLE{Koz:AiT85:9:r,
 author        = "Козякин, В. С.",
 title         = "О наблюдаемости периодических режимов, возникающих при
                  потере устойчивости положения равновесия импульсных
                  систем",
 journal       = "Автом. и телемех.",
 fjournal      = "Автоматика и телемеханика",
 year          = "1985",
 number        = "9",
 pages         = "42--48",
 url           = "https://mi.mathnet.ru/at7542",
 language      = "russian",
 annote        = "Потеря устойчивости положения равновесия импульсной системы
                  управления должна сопровождаться, согласно теоретическим
                  представлениям, рождением периодических режимов больших
                  периодов. Однако обнаружить эти режимы в эксперименте, как
                  правило, не удается. Выясняется причина этого кажущегося
                  противоречия. \par Малое изменение параметров, входящих в
                  систему управления, может привести к резкому, качественному
                  изменению ее свойств. Важным и распространенным примером
                  такой ситуации является потеря устойчивости положения
                  равновесия при прохождении параметров через некоторое
                  критическое значение. Знание форм потери устойчивости
                  необходимо при анализе систем управления; исследованию
                  этого вопроса посвящена обширная литература. В общем случае
                  потеря устойчивости положения равновесия системы
                  управления, зависящей от скалярного параметра,
                  сопровождается ответвлением от положения равновесия
                  инвариантного цикла. Это явление называется бифуркацией
                  Пуанкаре--Андронова--Хопфа. Потеря устойчивости положения
                  равновесия системы управления в общем случае должна
                  сопровождаться также~\cite{Koz:DAN77:232:r} бесконечной
                  серией последовательных ``рождений'' и следующих за ними
                  ``смертей'' периодических режимов сколь угодно больших
                  периодов. Это может привести к установлению (после ряда
                  сложных колебательных процессов) периодических режимов
                  любого достаточно большого периода. Ответвление
                  инвариантного цикла от положения равновесия наблюдается
                  часто. В то же время экспериментально обнаружить малые
                  периодические режимы больших периодов, как правило, не
                  удается. В работе выясняется причина этого кажущегося
                  противоречия между теорией и экспериментом.",
}

@INCOLLECTION{KozMTS:86:r,
 author        = "Козякин, В. С.",
 editor        = "Красносельский, М. А.",
 title         = "Критерии конечной определенности",
 booktitle     = "Математическая теория систем",
 chapter       = "8",
 publisher     = "Наука",
 address       = "М.",
 year          = "1986",
 pages         = "136--160",
 doi           = "10.13140/RG.2.1.2333.0402",
 language      = "russian",
 annote        = "Анализ задач математической теории систем связан с изучением
                  структуры множества решений нелинейных уравнений. Как
                  правило, нелинейные уравнения сложны для исследования и их
                  приходится каким-либо способом ``упрощать''. В одних
                  случаях это приводит к правильным выводам о строении
                  множества решений исходных уравнений, в других --- к
                  ложным. Часто интерес представляют малые решения уравнений.
                  В этом случае распространенным способом упрощения уравнений
                  является их усечение, т.е. отбрасывание в степенных
                  разложениях левых частей слагаемых высоких степеней.
                  Переход к усеченным уравнениям аналогичен анализу
                  устойчивости по первому приближению, анализу бифуркаций в
                  нелинейных задачах переходом к линеаризованным уравнениям и
                  др. В главе изучается вопрос о допустимости усечения при
                  исследовании систем вещественных нелинейных уравнений.",
}

@ARTICLE{Koz:DAN90:312:r,
 author        = "Козякин, В. С.",
 title         = "Абсолютная устойчивость дискретных рассинхронизованных
                  систем",
 journal       = "Докл. АН СССР",
 fjournal      = "Доклады АН СССР",
 year          = "1990",
 volume        = "312",
 number        = "5",
 pages         = "1066--1070",
 url           = "https://mi.mathnet.ru/dan6589",
 language      = "russian",
 annote        = "Проблеме абсолютной устойчивости положения равновесия
                  посвящены многочисленные публикации. При анализе дискретных
                  систем \[x(n + 1) = A(n)x(n) +f[n, x(n)],\quad x(n)\in
                  R^{n},\tag{$*$}\] в большинстве работ рассматривается
                  случай, когда $A(n)\equiv A$, причем спектр матрицы $A$
                  лежит в единичном круге, а слагаемое $f(n,x)$ в
                  определенном смысле мало по спавнеию с отображением
                  $A(n)x(n)\equiv Ax$. Начавшееся в последние годы изучение
                  рассинхронизованных систем управления стимулировало интерес
                  к проблеме абсолютной устойчивости систем ($*$) с сильно
                  меняющейся линейной частью. В этой ситуации возможности
                  традиционных методов теории абсолютной устойчивости резко
                  сужаются. В то же время задача об абсолютной устойчивости
                  оказывается содержательной и нетривиальной уже в случае
                  линейных систем ($*$) с переменной правой частью.",
}

@ARTICLE{Koz:AiT90:6:r,
 author        = "Козякин, В. С.",
 title         = "Алгебраическая неразрешимость задачи об абсолютной
                  устойчивости рассинхронизованных систем",
 journal       = "Автом. и телемех.",
 fjournal      = "Автоматика и телемеханика",
 year          = "1990",
 number        = "6",
 pages         = "41--47",
 url           = "https://mi.mathnet.ru/at5386",
 language      = "russian",
 annote        = "В сложных системах управления, содержащих импульсные
                  элементы, возможна рассинхронизация моментов включения этих
                  элементов. В ряде случаев несинхронный характер
                  срабатывания импульсных элементов не влияет на устойчивость
                  системы. В других случаях сколь угодно малая
                  рассинхронизация моментов включения импульсных элементов
                  приводит к резким изменениям динамики системы управления, и
                  система теряет устойчивость. В последние годы начато
                  интенсивное изучение эффектов, связанных с
                  рассинхронизацией систем управления; получены как
                  необходимые, так и достаточные условия устойчивости
                  различных классов рассинхронизованных систем. В то же время
                  найти общие, эффективно проверяемые критерии устойчивости
                  рассинхронизованных систем, аналогичные известным для
                  синхронизованных систем, не удалось. Задача об устойчивости
                  линейных рассинхронизованных систем оказалась более
                  сложной, чем задача об устойчивости синхронизованных
                  систем. В настоящей статье предпринимается попытка
                  формального объяснения сложности задачи исследования
                  устойчивости линейных рассинхронизованных систем.
                  Показывается, что критерия абсолютной устойчивости линейных
                  рассинхронизованных систем, заключающегося в конечном числе
                  арифметических действий, не существует.",
}

@ARTICLE{Koz:AiT90:10:r,
 author        = "Козякин, В. С.",
 title         = "Об абсолютной устойчивости систем с несинхронно работающими
                  импульсными элементами",
 journal       = "Автом. и телемех.",
 fjournal      = "Автоматика и телемеханика",
 year          = "1990",
 number        = "10",
 pages         = "56--63",
 url           = "https://mi.mathnet.ru/at5981",
 language      = "russian",
 annote        = "Понятие абсолютной устойчивости естественно возникает при
                  анализе систем управления, нелинейные характеристики
                  отдельных звеньев которых известны неточно или в силу
                  каких-то причин определяются неоднозначно. На динамику
                  систем управления с импульсными элемент также оказывают
                  влияние не только свойства звеньев, но и моменты
                  срабатывания импульсных элементов. Методы анализа систем с
                  синхронно работающими импульсными элементами достаточно
                  хорошо развиты. Отчасти этим и объясняется стремление к
                  синхронизации работы элементов при конструировании
                  дискретных систем. В то же время во многих случаях
                  приходится иметь дело с системами, импульсные элементы
                  которых срабатывают, вообще говоря, несинхронно. Такая
                  ситуация возникает, например, когда моменты срабатывания
                  импульсных элементов могут изменяться под воздействием
                  каких-либо внешних факторов. Тогда, чтобы гарантировать
                  устойчивость системы управления, необходимо рассмотреть
                  некоторый класс систем с одинаковыми функциональными
                  элементами и структурными связями между ними, но различными
                  наборами моментов срабатывания импульсных элементов. Этот
                  подход естественным образом приводит к понятию абсолютной
                  устойчивости в классе систем со всеми возможными (или
                  некоторыми) рассинхронизациями моментов срабатывания
                  импульсных элементов.\par В работе вводится понятие
                  абсолютной устойчивости систем по отношению к различным
                  классам рассинхронизации моментов срабатывания импульсных
                  элементов. Устанавливаются общие критерии абсолютной
                  устойчивости, родственные принципу отсутствия ограниченных
                  решений Красносельского--Покровского.",
}

@ARTICLE{Koz:DAN90:311:r,
 author        = "Козякин, В. С.",
 title         = "Об анализе устойчивости рассинхронизованных систем методами
                  символической динамики",
 journal       = "Докл. АН СССР",
 fjournal      = "Доклады АН СССР",
 year          = "1990",
 volume        = "311",
 number        = "3",
 pages         = "549--552",
 url           = "https://mi.mathnet.ru/dan6694",
 language      = "russian",
 annote        = "Динамика автономных систем управления с импульсными звеньями
                  описывается уравнениями, \[x_{i}(T_{ij}+0)=
                  f_{i}[x_{1}(T_{ij}-0),\ldots,x_{k}(T_{ij}-0)],\quad
                  i=1.....k,\tag{$*$}\] где каждая вектор-функция $x_{i}(y)$
                  со значениями в $R^{n_{i}}$ постоянна на интервалах $T_{ij}
                  < t < T_{ij+1}$ В классической теории импульсных систем
                  моменты переключения $T_{ij}$ различных компонент $x_{i}$
                  совпадают: $T_{1j}=T_{2j}=\cdots=T_{kj}$. Для этого случая
                  разработан богатый арсенал методов анализа динамики систем
                  ($*$). В последнее время начато исследование более сложной
                  ситуации, когда различные компоненты системы ($*$) могут
                  переключаться несинхронно, т.е. когда соотношения
                  $T_{1j}=T_{2j}=\cdots=T_{kj}$, вообще говоря, не
                  выполняются. Традиционные методы анализа оказываются плохо
                  приспособленными для исследования рассинхронизованных
                  систем; требуются новые идеи и новые подходы. Важный класс
                  составляют фазочастотно рассинхронизованные системы ($*$) с
                  моментами переключения $T_{ij}=\varphi_{i}+j\omega_{i}$.
                  Безвременно ушедший А.Ф.~Клепцын заметил, что устойчивость
                  таких систем тесно связана со свойствами
                  последовательностей символов, называемых ниже сдвиговыми
                  текстами. Это наблюдение позволило получить важные теоремы
                  об устойчивости линейных двухкомпонентных фазочастотно
                  рассинхронизованных систем управления. В работе проводится
                  символический анализ сдвиговых текстов, с помощью которого
                  получены утверждения об устойчивости нелинейных
                  рассинхронизованных систем. Развитый подход позволяет дать
                  простые доказательства теорем А.Ф.~Клепцына.",
}

@ARTICLE{Koz:AiT90:8:r,
 author        = "Козякин, В. С.",
 title         = "Об устойчивости фазочастотно рассинхронизованных систем при
                  возмущении моментов переключения компонент",
 journal       = "Автом. и телемех.",
 fjournal      = "Автоматика и телемеханика",
 year          = "1990",
 number        = "8",
 pages         = "35--42",
 url           = "https://mi.mathnet.ru/at5561",
 language      = "russian",
 annote        = "Чем сложнее структура системы управления с дискретными
                  элементами, тем труднее согласовать временные параметры
                  функционирования элементов этой системы. К нарушениям
                  согласованности работы дискретных элементов могут привести
                  также различные внешние факторы. В связи с этим в последние
                  годы все более пристальное внимание привлекают системы
                  управления, отдельные подсистемы которых могут выполнять
                  свои функции автономно, обмениваясь информацией друг с
                  другом с определенной периодичностью, определяемой не
                  централизованно, а внутренними параметрами соответствующих
                  подсистем. В этом случае подсистемы могут действовать
                  несинхронно друг с другом. Эта ситуация изучена слабо. Она
                  порождает вопросы о свойствах систем с несинхронно
                  действующими подсистемами. Первые же попытки
                  математического анализа динамики рассинхронизованных систем
                  управления показали, что сколь угодно малая
                  рассинхронизация изначально синхронизованных систем может
                  привести к потере устойчивости. Кажущееся удивительным, это
                  явление, возможно, станет более понятным, если заметить,
                  что факт синхронности взаимодействия элементов системы
                  математически выражается соотношениями, аналогичными
                  соотношениям резонанса в механике. Но, как известно,
                  наличие резонансов в механических системах может резко
                  ухудшить свойства этих систем, и, наоборот, механические
                  системы без резонансов обладают рядом замечательных
                  свойств. Если воспользоваться приведенной аналогией, то
                  можно ожидать, что как раз рассинхронизованные системы
                  управления должны в каких-то ситуациях быть лучше
                  синхронизованных систем.\par В работе изучается вопрос об
                  асимптотической устойчивости двухкомпонеитных фазочастотпо
                  рассинхронизованных систем управления. Показывается, что
                  малое возмущение периодов и фаз переключения компонент не
                  приводит к потере асимптотической устойчивости, если
                  невозмущепная система была асимптотически устойчива и
                  периоды переключения ее компонент были несоизмеримы.",
}

@ARTICLE{Koz:DAN91:r,
 author        = "Козякин, В. С.",
 title         = "О возмущении линейных рассинхронизованных систем",
 journal       = "Докл. АН СССР",
 fjournal      = "Доклады АН СССР",
 year          = "1991",
 volume        = "316",
 number        = "1",
 pages         = "54--57",
 url           = "https://mi.mathnet.ru/dan6267",
 language      = "russian",
 annote        = "В последние годы пристальное внимание привлекают системы,
                  отдельные части или элементы которых функционируют в
                  определенной степени автономно. Примерами являются системы
                  управления с независимо работающими импульсными элементами,
                  сети ЭВМ, многопроцессорные комплексы и т.п. Особенностью
                  таких систем является возможная нссинхронность работы их
                  частей. Для синхронизации работы частей системы иногда
                  принимают специальные меры. Если же синхронизация
                  невозможна, то имеют дело с рассинхронизованными, или, как
                  еще говорят, асинхронными системами. Если при этом способ
                  рассинхронизации неизвестен, то естественно возникает
                  вопрос об абсолютной устойчивости систем в классе всех
                  рассинхронизаций. В работе предлагается ответ на
                  принципиальный вопрос об условиях сохранения свойства
                  абсолютной устойчивости при малых возмущениях линейных
                  рассинхронизованных систем.",
}

@ARTICLE{Koz:AiT91:r,
 author        = "Козякин, В. С.",
 title         = "Об устойчивости линейных рассинхронизованных систем с
                  несимметрическими матрицами",
 journal       = "Автом. и телемех.",
 fjournal      = "Автоматика и телемеханика",
 year          = "1991",
 number        = "7",
 pages         = "52--58",
 url           = "https://mi.mathnet.ru/at4221",
 language      = "russian",
 annote        = "В публикациях последних лет растет число примеров явлений,
                  ситуаций и процессов, которые могут быть описаны в терминах
                  так называемых рассинхронизованных или, как еще говорят,
                  асинхронных систем. Математические проблемы, связанные с
                  анализом динамики рассинхронизованных систем, оказались
                  весьма трудными. Многие принципиальные и естественные
                  вопросы, достаточно простые в случае синхронизованных
                  систем, для рассинхронизованных систем открыты до сих пор.
                  Одним из них является вопрос о сохранении свойства
                  асимптотической устойчивости при малых возмущениях матриц
                  линейных рассин хронизованных систем. Этому вопросу, а
                  также тесно связанному с ним вопросу об устойчивости
                  рассинхронизованных систем при постоянно действующих
                  возмущениях посвящена настоящая статья. В ней
                  устанавливается новый признак асимптотической устойчивости
                  линейных рассинхронизованных систем. Показывается, что
                  проблема сохранения абсолютной асимптотической устойчивости
                  при малых возмущениях матриц линейных рассинхронизованных
                  систем равносильна проблеме устойчивости при постоянно
                  действующих возмущениях.",
}

@UNPUBLISHED{Koz96,
 author        = "Козякин, В. С.",
 title         = "Спектральные критерии абсолютной устойчивости
                  квазиуправляемых линейных систем",
 year          = "1996",
 pagetotal     = "11",
 doi           = "10.13140/RG.2.2.34877.26081",
 language      = "russian",
 note          = "Не опубликовано, 11 стр., 1996 г.",
 annote        = "Предлагается новый критерий абсолютной устойчивости линейных
                  систем, динамика которых описывается разностным уравнением
                  $x(n+1)=A(n)x(n),$ где при каждом значении $n$ матрицы
                  $A(n)$ принадлежат некоторому квазиуправляемому семейству
                  матриц $\mathcal{A}$. Условие устойчивости выражается в
                  терминах спектральных радиусов всевозможных конечных
                  произведений матриц из $\mathcal{A}$.",
}

@ARTICLE{Koz:AiT03:9:r,
 author        = "Козякин, В. С.",
 title         = "О неопределимости в о-минимальных структурах конечных
                  наборов матриц, бесконечные произведения которых сходятся,
                  ограничены или неограниченны",
 journal       = "Автом. и телемех.",
 fjournal      = "Автоматика и телемеханика",
 year          = "2003",
 number        = "9",
 pages         = "24--41",
 url           = "https://mi.mathnet.ru/at1939",
 language      = "russian",
 annote        = "Обобщаются результаты работы~\cite{Koz:AiT90:6:r}.
                  Рассматривается задача о сходимости, ограниченности или
                  неограниченности множества всех возможных произведений
                  матриц с сомножителями из некоторой конечной совокупности,
                  к которой сводятся многие вопросы теории управления и
                  математики. Установлена неопределимость данной задачи в
                  $o$-ми\-ни\-маль\-ных структурах, содержащих
                  полуалгебраические множества, что может рассматриваться как
                  характеристика сложности задачи. Из полученного результата
                  следует, в частности, что решение рассматриваемой задачи не
                  может быть получено как конечная булева комбинация условий,
                  включающих конечное число не только обычных арифметических
                  операций сложения, вычитания и умножения, но и взятия
                  экспоненты, а также применения ограниченных аналитических
                  функций.",
}

@ARTICLE{Koz:INFOPROC05-2:r,
 author        = "Козякин, В. С.",
 title         = "Штурмовы последовательности, генерируемые сохраняющими
                  ориентацию отображениями окружности",
 journal       = "Информационные процессы",
 year          = "2005",
 volume        = "5",
 number        = "4",
 pages         = "271--282",
 url           = "http://www.jip.ru/2005/271-282.pdf",
 language      = "russian",
 annote        = "Известно, что гомеоморфизмы окружности обладают множеством
                  нетривиальных и сильных свойств. В то же время требование
                  непрерывности отображения окружности в ряде приложений
                  может оказаться ограничительным. В связи с этим
                  актуальность приобретает вопрос о выделении такого класса
                  отображений окружности, который с одной стороны был бы
                  достаточно широким и содержал бы не только непрерывные
                  отображения, а с другой --- унаследовал бы как можно
                  большее число принципиальных свойств гомеоморфизмов
                  окружности. Ясно, что отказ от требования непрерывности
                  отображения окружности неизбежно приводит к потере ряда
                  свойств, присущих гомеоморфизмам окружности. Тем не менее,
                  как оказывается, разрывные отображения окружности,
                  сохраняющие ориентацию, обладают многими ``символическими''
                  свойствами, присущими гомеоморфизмам окружности.",
}

@ARTICLE{Koz:INFOPROC05:r,
 author        = "Козякин, В. С.",
 title         = "Экстремальные нормы, разрывные отображения окружности и
                  контрпример к гипотезе {Л}агариаса--{В}анга о конечности",
 journal       = "Информационные процессы",
 year          = "2005",
 volume        = "5",
 number        = "4",
 pages         = "301--335",
 url           = "http://www.jip.ru/2005/301-335.pdf",
 language      = "russian",
 annote        = "В 1995г. Дж.~Лагариас и Янг Ванг высказали предположение о
                  том, что обобщенный спектральный радиус конечного набора
                  матриц всегда достигается на некотором конечном
                  произведении матриц. Первый контрпример к этой ``гипотезе о
                  конечности'' был построен в 2002г. Т.~Бушем и Ж.~Мерессом,
                  а соответствующее доказательство существоенно опиралось на
                  конструкции теории меры. В 2003г. В.~Блондель,
                  А.~Владимиров и Ж.~Тэсс представили другое доказательство
                  контрпримера к гипотезе о конечности, которое было основано
                  на комбинаторных свойствах перестановок произведений
                  положительных матриц.\par В теории динамических систем
                  обобщенный спектральный радиус используется, в основном,
                  для описания скорости сходимости или расходимости
                  траекторий, описываемых произведениями матриц. В связи с
                  этим, упомянутые выше методы построения контрпримера к
                  гипотезе о конечности не совсем удовлетворительны (с точки
                  зрения автора, конечно), поскольку они не дают достаточно
                  конструктивного описания структуры траекторий с
                  максимальной скоростью роста (или минимальной скоростью
                  убывания).\par В статье предлагается еще одно
                  доказательство контрпримера к гипотезе о конечности,
                  выполненное в достаточно традиционной манере теории
                  динамических систем. Предложено описание траекторий с
                  максимальной скоростью роста в терминах так называемых
                  экстремальных норм Н.~Барабанова и связанных с ними
                  экстремальных траекторий. Конструкция контрпримера основана
                  на детальном анализе свойств экстремальных норм наборов
                  двумерных положительных матриц и существенно использует
                  технику символов Грама, позаимствованную из работы Т.~Буша
                  и Ж.~Мересса. Наконец, важную роль в доказательстве играют
                  понятие и свойства числа вращения для разрывных сохраняющих
                  ориентацию отображений окружности.",
}

@ARTICLE{Koz:INFOPROC06:r,
 author        = "Козякин, В. С.",
 title         = "Структура экстремальных траекторий дискретных линейных
                  систем и гипотеза {Л}агариаса--{В}анга о конечности",
 journal       = "Информационные процессы",
 year          = "2006",
 volume        = "6",
 number        = "4",
 pages         = "327--363",
 url           = "http://www.jip.ru/2006/327-363-2006.pdf",
 language      = "russian",
 annote        = "В 1995г. Дж.~Лагариас и Янг Ванг высказали предположение о
                  том, что обобщенный спектральный радиус конечного набора
                  матриц всегда достигается на некотором конечном
                  произведении матриц. Первый контрпример к этой ``гипотезе о
                  конечности'' был построен в 2002г. Т.~Бушем и Ж.~Мерессом,
                  а соответствующее доказательство существенно опиралось на
                  конструкции теории меры. В 2003г. В.~Блондель,
                  А.~Владимиров и Ж.~Тэсс представили доказательство
                  контрпримера к гипотезе о конечности, основанное на
                  комбинаторных свойствах перестановок произведений
                  положительных матриц.\par В теории управления и общей
                  теории динамических систем обобщенный спектральный радиус
                  используется для описания скорости сходимости или
                  расходимости траекторий, описываемых произведениями матриц.
                  В этом контексте упомянутые выше методы построения
                  контрпримера к гипотезе о конечности оказываются не вполне
                  удовлетворительными (с точки зрения автора, конечно),
                  поскольку они не дают достаточно конструктивного описания
                  структуры траекторий с максимальной скоростью роста (или
                  минимальной скоростью убывания).\par В связи с этим в
                  2005г. автором настоящей статьи было
                  предложено~\cite{Koz:INFOPROC05:r} еще одно доказательство
                  контрпримера к гипотезе о конечности, выполненное в духе
                  теории динамических систем. К сожалению, предложенный
                  подход не охватывал того класса матриц, для которого был
                  построен контрпример В.~Блонделем, А.~Владимировым и
                  Ж.~Тэссом. В настоящей работе восполняется этот пробел, что
                  потребовало существенной переработки доказательств.",
}

@ARTICLE{Koz:DAN09:r,
 author        = "Козякин, В. С.",
 title         = "О вычислительных аспектах теории совместного спектрального
                  радиуса",
 journal       = "Докл. АН",
 fjournal      = "Доклады АН",
 year          = "2009",
 volume        = "427",
 number        = "2",
 pages         = "160--164",
 language      = "russian",
 annote        = "Различные задачи теории управления, неавтономных и
                  многозначных линейных динамических систем, теории вейвлетов
                  и многих других разделов математики приводят к
                  необходимости анализа скорости роста матричных произведений
                  с сомножителями из некоторого набора матриц. Одной из
                  характеристик, описывающих экспоненциальную скорость роста
                  произведений матриц, является так называемый совместный или
                  обобщенный спектральный радиус. Вопросу получения
                  эффективных оценок совместного спектрального радиуса
                  посвящена настоящая работа.\par Пусть
                  $\mathscr{A}=\{A_{1},A_{2},\ldots,A_{r}\}$ --- набор
                  $d\times d$ матриц с элементами из поля $\mathbb{K}$
                  вещественных или комплексных чисел. Через $\mathscr{A}^{n}$
                  обозначим множество всех произведений матриц из
                  $\mathscr{A}$, состоящих из $n$ сомножителей. Если в
                  ${\mathbb{K}}^{d}$ задана некоторая норма $\|\cdot\|$, то
                  предел \[ \rho(\mathscr{A})=
                  \varlimsup_{n\to\infty}\|\mathscr{A}^{n}\|^{\frac{1}{n}},\tag{$*$}\]
                  где
                  $\|\mathscr{A}^{n}\|=\max\limits_{A\in\mathscr{A}^{n}}\|A\|$,
                  называется совместным спектральным радиусом набора матриц
                  $\mathscr{A}$.\par Для вычисления $\rho({\mathscr{A}})$
                  были предложены различные алгоритмы. К сожалению, ни один
                  из них не дает априорной оценки числа шагов, требуемых для
                  достижения заданной точности приближения
                  $\rho({\mathscr{A}})$. В связи с этим остается актуальной
                  задача получения явных оценок аппроксимации величины
                  $\rho(\mathscr{A})$. Кроме того, во многих приложениях
                  важны оценки скорости сходимости именно в обобщенной
                  формуле Гельфанда ($*$), имеющей прозрачную интерпретацию в
                  теории динамических систем.\par Целью настоящей работы
                  является получение явной оценки скорости сходимости величин
                  $\|\mathscr{A}^{n}\|^{\frac{1}{n}}$ к обобщенному
                  спектральному радиусу $\rho(\mathscr{A})$. В работе также
                  предлагаются две итерационные процедуры, позволяющие не
                  только вычислять с любой наперед заданной степенью точности
                  совместный спектральный радиус, но и одновременно
                  производить приближенное построение так называемых норм
                  Барабанова соответствующих наборов матриц.",
}

@ARTICLE{Koz:DAN10:r,
 author        = "Козякин, В. С.",
 title         = "Полиномиальные критерии v-достаточности струй в классах
                  отображений конечной гладкости",
 journal       = "Докл. АН",
 fjournal      = "Доклады АН",
 year          = "2010",
 volume        = "430",
 number        = "5",
 pages         = "596--599",
 language      = "russian",
 annote        = "Многие задачи нелинейного анализа могут быть сведены к
                  исследованию структуры множества решений недоопределенных
                  нелинейных уравнений \[ f(x)=0,\tag{$*$} \] в которых
                  $f:\mathbb{R}^{n}\to \mathbb{R}^{m}$, $n\ge m$ и $f(0)=0$.
                  Исследование решений нелинейных уравнений даже в малой
                  окрестности нулевого решения часто оказывается достаточно
                  сложным, и поэтому соответствующие уравнения приходится
                  каким-либо способом упрощать. Одним из распространенных
                  способов такого упрощения является так называемое
                  ``усечение'' уравнения ($*$). Формально, для
                  $C^{k}$-гладкого отображения $f$ под $r$-усечением при
                  $r\leq k$ понимается его отрезок разложения Тейлора в нуле
                  $f^{(r)}(x)$, в котором удержаны только слагаемые степеней,
                  не превосходящих $r$.\par Простые примеры показывают, что
                  множества решений уравнения ($*$) и усеченного уравнения \[
                  f^{(r)}(x)=0\tag{$**$} \] могут оказаться топологически
                  различными. Тогда естественно возникает вопрос о том, при
                  каких условиях множества решений уравнений ($*$) и ($**$)
                  локально топологически эквивалентны друг другу. Этот вопрос
                  тесно связан с проблемой достаточности струй
                  отображений.\par Получены полиномиальные критерии
                  достаточности, которые могут трактоваться как естественное
                  обобщение известных условий Койпера-Куо, а также условия
                  Тома.",
}

@ARTICLE{Koz:INFOPROC15:r,
 author        = "Козякин, В. С.",
 title         = "Об асимптотике косинус-рядов нескольких переменных со
                  степенными коэффициентами",
 journal       = "Информационные процессы",
 year          = "2015",
 volume        = "15",
 number        = "2",
 pages         = "128--133",
 url           = "http://www.jip.ru/2015/128-133-2015.pdf",
 language      = "russian",
 annote        = "Исследование асимптотического поведения тригонометрических
                  рядов в окрестности нулевой точки представляет важный
                  раздел математического анализа. Для тригонометрических
                  рядов от одной переменной эта проблема была исчерпывающе
                  изучена различными авторами в серии публикаций, восходящих
                  к работе Дж.~Харди 1928-го года. Тригонометрические ряды
                  нескольких переменных в этом отношении оказались менее
                  исследованными. Цель работы --- найти асимптотики для
                  тригонометрических рядов нескольких переменных с членами,
                  имеющими вид ``единица минус косинус'' с точностью до
                  убывающего степенного коэффициента.",
}

@ARTICLE{Koz:INFOPROC16:r,
 author        = "Козякин, В. С.",
 title         = "Конструктивная устойчивость и стабилизируемость
                  положительных линейных переключающихся систем с дискретным
                  временем",
 journal       = "Информационные процессы",
 year          = "2016",
 volume        = "16",
 number        = "2",
 pages         = "194--206",
 url           = "http://www.jip.ru/2016/194-206-2016.pdf",
 language      = "russian",
 annote        = "Описывается новый класс линейных асинхронных положительных
                  систем с дискретным временем, для которых задачи
                  устойчивости и стабилизируемости допускают конструктивное
                  решение. Системы, образующие этот класс, могут
                  рассматриваться как естественное обобщение систем с так
                  называемыми независимо переключающимися координатами
                  векторов состояния. Отличительной особенностью таких систем
                  является то, что образующие их асинхронные блоки допускают
                  произвольное последовательно-параллельное
                  ``пересоединение'' без потери свойства ``конструктивной
                  разрешимости'' проблем устойчивости или стабилизируемости
                  системы. Показано также, что для таких систем допустимо
                  конструктивное построение индивидуальных ``положительных''
                  траекторий с наибольшей или наименьшей скоростью
                  роста/стремления к нулю.",
}

@ARTICLE{Koz:INFOPROC19:r,
 author        = "Козякин, В. С.",
 title         = "Осторожно, DOI! : ``Библиографический детектив'' эпохи
                  цифровизации",
 journal       = "Информационные процессы",
 year          = "2019",
 volume        = "19",
 number        = "1",
 pages         = "54--59",
 url           = "http://www.jip.ru/2019/54-59-2019.pdf",
 language      = "russian",
 annote        = "Описывается пример несоответствия информации,
                  предоставляемой популярными библиографическими сервисами, и
                  обсуждаются причины такого несоответствия.",
}

@ARTICLE{Koz:INFOPROC23:r,
 author        = "Козякин, В. С.",
 title         = "Конвертер библиографии из формата {BibTEX} в формат
                  {AMSBIB}",
 journal       = "Информационные процессы",
 year          = "2023",
 volume        = "23",
 number        = "4",
 pages         = "455--469",
 url           = "http://www.jip.ru/2023/455-469-2023.pdf",
 language      = "russian",
 annote        = "Описывается система преобразования библиографии из формата
                  Bib\TeX{} в формат AMSBIB, рекомендованный общероссийским
                  порталом Math-Net.Ru для использования при подготовке
                  библиографии в публикациях в российских журналах
                  математической направленности. Осуществление такого
                  преобразования сводится к применению стандартной процедуры
                  создания библиографии с помощью системы BibTEX.",
}

@MISC{KozPreRu24-2,
 author        = "Козякин, В. С.",
 title         = "Аннотированная библиография по сходимости матричных
                  произведений и теории совместного/обобщенного спектрального
                  радиуса",
 howpublished  = "PREPRINTS.RU",
 year          = "2024",
 doi           = "10.24108/preprints-3113114",
 language      = "russian",
 note          = "\url{https://preprints.ru/article/1418}",
 annote        = "Проблематика оценки скорости роста/убывания матричных
                  произведений при стремлении числа сомножителей к
                  бесконечности возникает в разнообразных приложениях и уже
                  более полувека привлекает внимание исследователей. К
                  сожалению, сколько-нибудь систематическое изложение
                  соответствующей теории до настоящего времени практически
                  отсутствует, что в определенной степени объясняется
                  разнообразием используемых в данной теории методов из самых
                  разных областей математики, а также постоянно появляющимися
                  новыми значительными результатами, зачастую публикуемыми в
                  журналах самой неожиданной направленности. Чтобы упростить
                  ориентацию исследователей автор и попытался максимально
                  полно отразить сведения, относящиеся к данному кругу
                  вопросов, пусть даже в достаточно несовершенной форме
                  аннотаций к публикациям.",
}

@MISC{KozPreRu24-1,
 author        = "Козякин, В. С.",
 title         = "Пример двух разных максимизирующих спектр матричных
                  произведений с неравным числом одноименных сомножителей",
 howpublished  = "PREPRINTS.RU",
 year          = "2024",
 doi           = "10.24108/preprints-3113112",
 language      = "russian",
 note          = "\url{https://preprints.ru/article/1416}",
 annote        = "Недавно J.~Bochi и P.~Laskawiec построили пример множества
                  матриц $\{A,B\}$, обладающего двумя различными (с точностью
                  до циклических перестановок сомножителей) произведениями
                  матриц $AABABB$ и $BBABAA$, максимизирующими спектр. В
                  настоящей работе выделяется класс матричных множеств,
                  обладающих тем свойством, что наличие в них хотя бы одного
                  матричного произведения с нечетным числом сомножителей,
                  максимизирующего спектр, автоматически влечет существование
                  еще одного матричного произведения, максимизирующего
                  спектр. При этом, в дополнение к примеру
                  Bochi--Laskawiec'а, количество одноименных сомножителей
                  (сомножителей вида $A$ или $B$) в этих произведениях матриц
                  оказывается различным. Работоспособность предложенного
                  подхода подтверждается построением примера множества
                  $2\times2$ матриц $\{A,B\}$, для которого произведения
                  матриц, максимизирующими спектр, имеют вид $BAA$ и $BBA$.",
}

@ARTICLE{KozKraRa:DAN06:r,
 author        = "Козякин, В. С. and Красносельский, А. М. and Рачинский, Д.
                  И.",
 title         = "О языках {А}рнольда в задаче о периодических траекторияx
                  больших амплитуд",
 journal       = "Докл. АН",
 fjournal      = "Доклады АН",
 year          = "2006",
 volume        = "411",
 number        = "3",
 pages         = "295--301",
 language      = "russian",
}

@ARTICLE{KozKra:AIT79:r,
 author        = "Козякин, В. С. and Красносельский, М. А.",
 title         = "К вопросу о влиянии малых запаздываний на динамику
                  нелинейных систем",
 journal       = "Автом. и телемех.",
 fjournal      = "Автоматика и телемеханика",
 year          = "1979",
 number        = "1",
 pages         = "5--8",
 url           = "https://mi.mathnet.ru/at5853",
 language      = "russian",
 annote        = "Рассматриваются нелинейные системы, динамика которых
                  качественно различна в зависимости от типа малых
                  запаздываний в каналах передачи информации.",
}

@ARTICLE{KozKra:ZHVMMF79:r,
 author        = "Козякин, В. С. and Красносельский, М. А.",
 title         = "О нескольких задачах, связанных с методом минимальных
                  невязок",
 journal       = "Ж. вычисл. матем. и матем. физ.",
 year          = "1979",
 volume        = "19",
 number        = "2",
 pages         = "508--510",
 url           = "https://mi.mathnet.ru/zvmmf5433",
 language      = "russian",
 annote        = "Рассматриваются две процедуры приближенного построения
                  решений систем линейных уравнений с несимметрическими
                  матрицами --- метод обычных итераций и метод минимальных
                  невязок. Проводится сравнение скоростей сходимости этих
                  процедур. В случае плохо обусловленных матриц формальные
                  оценки скорости сходимости требуют отдать предпочтение
                  методу простых итераций. В работе излагаются соображения,
                  противоречащие такому выводу.",
}

@ARTICLE{KozKra:DAN80:r,
 author        = "Козякин, В. С. and Красносельский, М. А.",
 title         = "Метод функционализации параметра в задаче о точках
                  бифуркации",
 journal       = "Докл. АН СССР",
 fjournal      = "Доклады АН СССР",
 year          = "1980",
 volume        = "254",
 number        = "5",
 pages         = "1061--1064",
 url           = "https://mi.mathnet.ru/dan43959",
 language      = "russian",
 annote        = "Проблеме ветвления и, в частности, бифуркации решений
                  различных задач (фигуры равновесия вращающейся жидкости,
                  потеря устойчивости упругих систем, возникновение волн на
                  поверхности жидкости, рождение автоколебательных режимов и
                  т.д.) посвящена обширная литература, начиная с классических
                  работ А.М.~Ляпунова, А.~Пуанкаре, Э.~Шмидта,
                  А.И.~Некрасова. В большинстве случаев для исследования
                  разветвляющихся решений используется та или иная
                  аналитическая техника. Известны и качественные методы;
                  например, для достаточно полного анализа точек бифуркации
                  часто достаточна весьма скромная информация лишь о
                  линеаризованных уравнениях. В статье предлагается общий
                  операторный подход к качественному исследованию точек
                  бифуркации для того важного случая, когда из нулевого
                  решения рождается сразу континуум ненулевых малых решений.
                  К таким задачам относится, например, проблема малых
                  автоколебаний автономных систем (так как вместе с каждым
                  периодическим режимом возможны режимы, полученные
                  произвольным изменением начальной фазы). Приложениям к
                  проблеме Андронова-Хопфа посвящена вторая часть статьи.",
}

@ARTICLE{KK:INFOPROC07:r,
 author        = "Козякин, В. С. and Кузнецов, Н. А.",
 title         = "Достоверность компьютерного моделирования с точки зрения
                  теории информации",
 journal       = "Информационные процессы",
 year          = "2007",
 volume        = "7",
 number        = "3",
 pages         = "323--368",
 url           = "http://www.jip.ru/2007/323-368-2007.pdf",
 language      = "russian",
 annote        = "В предлагаемой обзорной статье обсуждаются вопросы,
                  связанные с проблемами компьютерного моделирования
                  непрерывных объектов. Приводятся примеры, показывающие, что
                  даже в самых, казалось бы, тривиальных ситуациях результаты
                  компьютерного моделирования могут кардинально отличаться от
                  свойств исходных непрерывных объектов. Данный факт
                  усугубляется тем, что зачастую ситуация не может быть
                  исправлена повышением точности аппроксимации исходных
                  непрерывных объектов. Предлагаются математические модели,
                  позволяющие до известной степени объяснить возникающие
                  феномены, а также использовать и/или парировать их
                  негативные последствия.",
}

@ARTICLE{KKP:DAN96:r,
 author        = "Козякин, В. С. and Кузнецов, Н. А. and Покровский, А. В.",
 title         = "Феноменологическая модель статистик длин циклов и переходных
                  процессов дискретных динамических систем",
 journal       = "Докл. РАН",
 fjournal      = "Доклады РАН",
 year          = "1996",
 volume        = "349",
 number        = "2",
 pages         = "165--168",
 url           = "https://mi.mathnet.ru/dan4071",
 language      = "russian",
 annote        = "Компьютерное моделирование становится все более
                  распространенным методом исследования поведения
                  динамических систем, к которому часто прибегают тогда,
                  когда строгие теоретические методы анализа оказываются
                  неработоспособными, например, при исследовании систем с
                  элементами хаотического поведения. Однако хаотичность
                  проявляется обычно на достаточно длинных временных
                  интервалах и предполагает наличие бесконечного числа
                  непериодических траекторий. Компьютерная же модель является
                  отображением конечного множества в себя и любая ее
                  траектория становится периодической после некоторого
                  времени. В этой ситуации ожидать сходства эргодических
                  свойств исходной непрерывной системы и ее дискретной модели
                  можно лишь на промежутках времени не превышающих по порядку
                  величины длительности переходного процесса. Поэтому для
                  сравнительного анализа свойств исходной динамической
                  системы и ее компьютерной модели важно знание функций
                  распределения длин циклов и переходных процессов, доли
                  коллапсирующих элементов. Однако для систем со сложным
                  поведением указанные комбинаторные характеристики, как
                  правило, не могут быть вычислены непосредственно ни
                  теоретически, ни в компьютерном эксперименте. Кроме того,
                  они весьма чувствительны к выбору процедуры дискретизации,
                  что вынуждает рассматривать их усредненные значения по
                  отношению к некоторому ансамблю дискретизаций. Но даже и в
                  этом более простом случае их строгий анализ наталкивается
                  на существенные трудности, не преодоленные до настоящего
                  времени. В связи с этим, как компромиссный вариант,
                  представляют интерес феноменологические модели статистик
                  длин циклов, переходных процессов и других комбинаторных
                  характеристик дискретизаций рассматриваемых систем.\par К
                  сожалению, многие качественно вполне адекватные модели с
                  количественной точки зрения оказываются не вполне
                  удовлетворительными, что и явилось побудительным мотивом
                  введения в работе нового класса моделей,
                  продемонстрировавшего в численных экспериментах высокую
                  количественную точность.",
}

@ARTICLE{KKCh:AiT19:1:r,
 author        = "Козякин, В. С. and Кузнецов, Н. А. and Чеботарев, П. Ю.",
 title         = "Консенсус в асинхронных мультиагентных системах. I",
 journal       = "Автом. и телемех.",
 fjournal      = "Автоматика и телемеханика",
 year          = "2019",
 number        = "4",
 pages         = "3--40",
 doi           = "10.1134/S0005231019040019",
 url           = "https://mi.mathnet.ru/at15269",
 language      = "russian",
 annote        = "Представлен обзор результатов по моделям консенсуса в
                  асинхронных мультиагентных системах с дискретным и
                  непрерывным временем. Дается описание математических
                  методов, разработанных в последние годы, которые
                  используются при анализе проблем устойчивости,
                  стабилизируемости и консенсуса для линейных мультиагентных
                  систем с дискретным временем. В основе этих методов лежит
                  идея привлечения понятия совместного/обобщенного
                  спектрального радиуса наборов матриц для анализа скорости
                  сходимости матричных произведений с сомножителями из
                  множеств матриц со специальными свойствами.",
}

@ARTICLE{KKCh:AiT19:2:r,
 author        = "Козякин, В. С. and Кузнецов, Н. А. and Чеботарев, П. Ю.",
 title         = "Консенсус в асинхронных мультиагентных системах. II",
 journal       = "Автом. и телемех.",
 fjournal      = "Автоматика и телемеханика",
 year          = "2019",
 number        = "5",
 pages         = "3--31",
 doi           = "10.1134/S0005231019050015",
 url           = "https://mi.mathnet.ru/at15280",
 language      = "russian",
 annote        = "Описываются математические методы анализа устойчивости,
                  стабилизируемости и консенсуса линейных мультиагентных
                  систем с дискретным временем. В основе этих методов лежит
                  идея привлечения понятия совместного/обобщенного
                  спектрального радиуса наборов матриц для анализа скорости
                  сходимости матричных произведений с сомножителями из
                  множеств матриц со специальными свойствами. Работа
                  продолжает обзор авторов ``Консенсус в асинхронных
                  мультиагентных системах'', первая часть которого
                  опубликована в~\cite{KKCh:AiT19:1:r}.",
}

@ARTICLE{KKCh:AiT19:3:r,
 author        = "Козякин, В. С. and Кузнецов, Н. А. and Чеботарев, П. Ю.",
 title         = "Консенсус в асинхронных мультиагентных системах. III",
 journal       = "Автом. и телемех.",
 fjournal      = "Автоматика и телемеханика",
 year          = "2019",
 number        = "6",
 pages         = "3--37",
 doi           = "10.1134/S0005231019060011",
 url           = "https://mi.mathnet.ru/at15290",
 language      = "russian",
 annote        = "Описаны некоторые классы линейных асинхронных мультиагентных
                  систем с дискретным временем, для которых проблема
                  устойчивости допускает конструктивное решение. Описан также
                  общий аналитический подход к построению числовых
                  характеристик, аналогичных обобщенному спектральному
                  радиусу в теории устойчивости, которые предоставляли бы
                  возможность анализировать стабилизируемость управляемых
                  мультиагентных систем. Работа завершает обзор авторов
                  ``Консенсус в асинхронных мультиагентных системах'', первые
                  две части которого опубликованы
                  в~\cite{KKCh:AiT19:1:r,KKCh:AiT19:2:r}.",
}

@ARTICLE{KozPok:DAN92:r,
 author        = "Козякин, В. С. and Покровский, А. В.",
 title         = "Роль свойств типа управляемости в изучении устойчивости
                  рассинхронизованных динамических систем",
 journal       = "Докл. АН СССР",
 fjournal      = "Доклады АН СССР",
 year          = "1992",
 volume        = "324",
 number        = "1",
 pages         = "60--64",
 url           = "https://mi.mathnet.ru/dan5543",
 language      = "russian",
 annote        = "В последнее время значительное внимание уделяется анализу
                  устойчивости так называемых рассинхронизованных или
                  асинхронных систем. В работе изучаются геометрические
                  свойства совокупностей режимов рассинхронизованных систем,
                  обладающих специальными свойствами типа управляемости по
                  Калману. Показывается, что взаимосвязи между свойствами
                  устойчивости, асимптотической устойчивости и неустойчивости
                  указанных совокупностей аналогичны взаимосвязям между
                  соответствующими свойствами совокупности решений линейного
                  дифференциального или разностного уравнения в случае
                  простоты ведущего собственного значения матрицы,
                  определяющей это уравнение. Формулируемые ниже результаты
                  полезны и при анализе классической проблемы абсолютной
                  устойчивости. Излагаемый подход идейно близок к принципу
                  отсутствия ограниченных режимов в проблеме абсолютной
                  устойчивости.",
}

@ARTICLE{KozPok:IzRAEN97:r,
 author        = "Козякин, В. С. and Покровский, А. В.",
 title         = "Квазиуправляемость и оценка амплитуд переходных процессов в
                  дискретных системах",
 journal       = "Известия РАЕН, серия МММИУ",
 year          = "1997",
 volume        = "1",
 number        = "3",
 pages         = "128--150",
 language      = "russian",
 annote        = "Изучаются геометрические характеристики совокупностей
                  режимов систем управления, обладающих свойством
                  квазиуправляемости, родственным свойству управляемости по
                  Калману. Показывается, что взаимосвязи между устойчивостью,
                  асимптотической устойчивостью и неустойчивостью указанных
                  совокупностей аналогичны взаимосвязям между
                  соответствующими свойствами совокупностей решений линейного
                  дифференциального или разностного уравнения в случае
                  простоты ведущего собственного значения матрицы,
                  определяющей это уравнение. Предложен новый подход к оценке
                  величины перерегулирования переходных режимов в
                  квазиуправляемых системах, идейно близкий к принципу
                  отсутствия ограниченных режимов в проблеме абсолютной
                  устойчивости. Он заключается в получении априорных
                  конструктивных оценок степени перерегулирования переходных
                  режимов, получаемых в терминах так называемой меры
                  квазиуправляемости.",
}

@TECHREPORT{KraKozEm79:r,
 author        = "Красносельский, М. А. and Емелин, И. В. and Козякин, В. С.",
 title         = "Об итерационных процедурах в линейных задачах",
 institution   = "Институт проблем управления",
 address       = "М.",
 year          = "1979",
 pagetotal     = "64",
 type          = "Препринт",
 doi           = "10.13140/2.1.4044.5127",
 language      = "russian",
 annote        = "Излагаются результаты сравнительного анализа метода
                  минимальных невязок и метода обычных итераций приближенного
                  решения систем линейных уравнений с несимметрическими
                  матрицами, анализируется спурт-метод приближенного решения
                  систем линейных уравнений с симметрическими положительно
                  определенными матрицами, изучается возможность
                  регуляризации задачи приближенного решения некорректных
                  линейных уравнений при помощи итерационной процедуры со
                  специальным правилом останова.",
}

@INPROCEEDINGS{KKKP:Rousse81:r,
 author        = "Красносельский, М. А. and Козякин, В. С. and Красносельский,
                  А. М. and Покровский, А. В.",
 editor        = "Димовски, И. and Стоянова, Й.",
 title         = "О динамике систем регулирования с несколькими
                  нелинейностями",
 booktitle     = "Труды Второй Конференции ``Дифференциальные уравнения и
                  применения'', Руссе, Болгария, 29 июня -- 4 июля, 1981",
 organization  = "Высшее техническое училище им. А.~Кынчева -- Руссе, Центр
                  математики",
 address       = "Руссе, Болгария",
 year          = "1982",
 volume        = "I",
 pages         = "366--376",
 language      = "russian",
}

@ARTICLE{KK:RT08:r,
 author        = "Кузнецов, Н. А. and Козякин, В. С.",
 title         = "Теорема {К}отельникова --- основа цифрового оценивания и
                  моделирования непрерывных процессов",
 journal       = "Радиотехника",
 year          = "2008",
 volume        = "8",
 pages         = "8--14",
 url           = "https://www.researchgate.net/publication/266741497",
 language      = "russian",
 annote        = "Исследовано значение теоремы В. А. Котельникова для решения
                  практических задач восстановления непрерывных сигналов по
                  дискретным отсчетам. Рассмотрены вопросы потери информации
                  при дискретизации непрерывных сигналов по времени и в
                  пространстве.",
}

@INPROCEEDINGS{PYKMOP85,
 author        = "Посицельский, Е. Д. and Яровая, Е. Б. and Козякин, В. C. and
                  Метельская, В. А. and Овчинников, В. В. and Перова, Н. В.",
 title         = "Модель влияния гемосорбции на обмен липопротеидов плазмы
                  крови",
 booktitle     = "Всесоюзный семинар ``Математические и вычислительные методы
                  в биологии''",
 publisher     = "Пущино",
 year          = "1985",
 pages         = "148--150",
 language      = "russian",
}