Kozyakin, Victor Sergeevich

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Total publications: 35
Scientific articles: 34

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Main Scientist Researcher
Doctor of physico-mathematical sciences (1992)
Speciality: 01.01.11 (System analisys)
Birth date: 16.04.1950
Keywords: bifurcation; stability; attractors; dynamical systems; complex behavior; simulation; nonlinear systems; asynchronous systems; undecidability; discretization; topological methods.
UDC: 517.925, 517.929, 517.935, 517.938, 517.710, 517.988, 519.612, 62-504.12
MSC: 34Cxx, 34Dxx, 37Cxx, 37Dxx, 37Exx, 37Gxx, 39A12, 68R15, 70Kxx, 93Cxx, 93Dxx


Basic scientific interests are concentrated around problems of qualitative analysis of complex dynamical systems (stability, bifurcations, robustness with respect to perturbation of various kind) in situations when traditional in classic analysis suppositions about smoothness or continuity of dynamical systems under consideration, or about continuity of the state space or the "time component", are not satisfied. Together with M. A. Krasnosel'skii the method of parameter functionalization was developed which allowed to analyze bifurcations of steady states and periodic regimes (a kind of Hopf bifurcation) of non-smooth dynamical systems. Later, with utilization of this method the so-called effect of subfurcation was discovered, i.e. the effect of bifurcating short-living long-periodic regimes of nonsmooth dynamical system in situations when for their smooth analogs the bifurcation of invariant cycles takes place. There were developed essential principles of the theory of stability for the so-called asynchronous systems, i.e. systems describing dynamics of objects updating their states at discrete time instants asynchronously with each other (the typical example of such systems is the computational network). As a bypass result, the algebraic insolubility of the problem of stability analysis for the infinite products of matrices from a finite family was established. Methods of analysis of the dynamics of spatial discretizations for continuous dynamical systems were studied too.


In 1972 graduated from the Mathematical Faculty of the Voronezh State University where specialized in functional analysis, differential equations and control theory. In 1973–1976 studied at the post-graduate courses at the Institute for Control Problems of the Academy of Sciences of the USSR under the supervision of prof. M. A. Krasnosel'skii. The main direction of investigation was the analysis of bifurcation effects accompanying the loss of stability of equilibriums in autonomous or periodic differential or difference equations. It was discovered that typically the loss of stability of the equilibrium in multidimensional case is accompanied by generation of long-periodic solutions with unbounded periods at the moment of branching. This phenomenon got the name subfurcation. In 1976–1988 worked at the National Cardiology Research Center of the Academy of Medical Sciences of the USSR where concentrated on developing computer methods and algorithms for the electrocardiogram parameters measurement. Took part in development of the automated real-time system for diagnostic of cardiac rhythm disorders in the coronary care units. New algorithms were developed for the fast noise removing in electrocardiograms based on the ideas of median and hysteresis filtering. Algorithms for automatic measurement of the parameters of QRS-complexes and P-waves were developed, too, so as alogorithms for edge detection in isotopic images of the hart. Problems of real-time utilization of computer methods of measurement and computation gave a rise to theoretic investigation of asynchronous systems. In parallel, there were continued investigation of the problem of topological classification of singularities of sub-definite mappings. In 1988–1990 worked in the ecology department of the Research Institute for Control Problems "NPO ASU Moskva" where investigated the problem of stability of the phase and frequency desynchronized systems. There were developed symbolical methods of analysis of stability of frequency asynchronous systems. From 1990 until now worked at the Institute for Information Transmission Problems of the Russian Academy of Sciences where continued to investigate asynchronous systems. There were analyzed influence of the conditions of the controllability type on transitional regimes in asynchronous systems. Methods of the theory of stability of asynchronous systems were applied to analysis of flows in data networks and functioning of neural Hopfield-Tank networks. There were started an investigation of the problem of influence of spatial and temporal discretization on the properties of models of continuous systems. In 1979 got the degree of the Candidate of Physical and Mathematical Sciences (an equivalent of the Ph.D. in western countries) and in 1992 got the degree of the Doctor of Physical and Mathematical Sciences.

In different times was the member of Dissertation Soviets (dissertation's qualification board in Russia) at the Yaroslavl State University and at the Institute for Information Transmission Problems. An Associated Editor in the electronic journal "Information processes". Took part in several foreign research grants (Australia, Germany, NATO).

Main publications:
  • Kozyakin V., Krasnosel'skii M. The method of parameter functionalization in the Hopf bifurcation problem // Nonlinear Analysis, TMA, 1987, 11, 2, 149–161.
Full list of publications:

Publications in Math-Net.Ru
1. V. S. Kozyakin, N. A. Kuznetsov, P. Yu. Chebotarev, “Consensus in asynchronous multiagent systems. III. Constructive stability and stabilizability”, Avtomat. i Telemekh., 2019, 6,  3–27  mathnet  elib; Autom. Remote Control, 80:6 (2019), 989–1015  isi  scopus
2. V. S. Kozyakin, N. A. Kuznetsov, P. Yu. Chebotarev, “Consensus in asynchronous multiagent systems. II. Method of joint spectral radius”, Avtomat. i Telemekh., 2019, 5,  3–31  mathnet  elib; Autom. Remote Control, 80:5 (2019), 791–812  isi  scopus
3. V. S. Kozyakin, N. A. Kuznetsov, P. Yu. Chebotarev, “Consensus in asynchronous multiagent systems. I”, Avtomat. i Telemekh., 2019, 4,  3–40  mathnet  elib
4. V. S. Kozyakin, “Indefinability in o-Minimal Structures of Finite Sets of Matrices Whose Infinite Products Converge and Are Bounded or Unbounded”, Avtomat. i Telemekh., 2003, 9,  24–41  mathnet  mathscinet  zmath; Autom. Remote Control, 64:9 (2003), 1386–1400  isi  scopus
5. N. A. Kuznetsov, V. S. Kozyakin, A. V. Pokrovskii, “A phenomenological model of statistics of the lengths of cycles and transient processes of discretizations of dynamical systems”, Dokl. Akad. Nauk, 349:2 (1996),  165–168  mathnet  mathscinet  zmath
6. Ph. Diamond, P. Kloeden, V. S. Kozyakin, A. V. Pokrovskii, “Robustness of the observable behavior of semihyperbolic dynamic systems”, Avtomat. i Telemekh., 1995, 11,  148–159  mathnet  mathscinet  zmath; Autom. Remote Control, 56:11 (1995), 1627–1636
7. Ph. Diamond, P. Kloeden, V. S. Kozyakin, M. A. Krasnosel'skii, A. V. Pokrovskii, “Periodic trajectories of nonsmooth perturbations of systems with chaotic behavior”, Avtomat. i Telemekh., 1995, 5,  34–41  mathnet  mathscinet; Autom. Remote Control, 56:5 (1995), 637–643
8. Ph. Diamond, P. Kloeden, V. S. Kozyakin, M. A. Krasnosel'skii, A. V. Pokrovskii, “Structural stability of the trajectories of dynamical systems with respect to hysteresis perturbations”, Dokl. Akad. Nauk, 343:1 (1995),  25–27  mathnet  mathscinet  zmath
9. A. A. Vladimirov, V. S. Kozyakin, N. A. Kuznetsov, A. Mandelbaum, “Investigation of the dynamic complementarity problem by methods of the theory of desynchronized systems”, Dokl. Akad. Nauk, 329:1 (1993),  5–8  mathnet  mathscinet  zmath; Dokl. Math., 47:2 (1993), 169–173
10. V. S. Kozyakin, A. V. Pokrovskii, “The role of controllability-type properties in the study of the stability of desynchronized dynamical systems”, Dokl. Akad. Nauk, 324:1 (1992),  60–64  mathnet  mathscinet  zmath; Dokl. Math., 37:5 (1992), 213–215
11. V. S. Kozyakin, “On the stability of linear desynchronized systems with asymmetric matrices”, Avtomat. i Telemekh., 1991, 7,  52–58  mathnet  mathscinet  zmath; Autom. Remote Control, 52:7 (1991), 928–933
12. V. S. Kozyakin, “Perturbation of linear desynchronized systems”, Dokl. Akad. Nauk SSSR, 316:1 (1991),  54–57  mathnet  mathscinet  zmath; Dokl. Math., 36:1 (1991), 16–17
13. V. S. Kozyakin, “On absolute stability of systems with non-synchronous pulse elements”, Avtomat. i Telemekh., 1990, 10,  56–63  mathnet  mathscinet  zmath; Autom. Remote Control, 51:10 (1990), 1349–1355
14. V. S. Kozyakin, “Stability of phase-frequency desynchronized systems under component switching time disturbances”, Avtomat. i Telemekh., 1990, 8,  35–41  mathnet  mathscinet  zmath; Autom. Remote Control, 51:8 (1990), 1034–1040
15. V. S. Kozyakin, “Algebraic unsolvability of a problem on the absolute stability of desynchronized systems”, Avtomat. i Telemekh., 1990, 6,  41–47  mathnet  mathscinet  zmath; Autom. Remote Control, 51:6 (1990), 754–759
16. V. S. Kozyakin, “Absolute stability of discrete desynchronized systems”, Dokl. Akad. Nauk SSSR, 312:5 (1990),  1066–1070  mathnet  mathscinet  zmath; Dokl. Math., 35:6 (1990), 518–519
17. V. S. Kozyakin, “Analysis of the stability of desynchronized systems by methods of symbolic dynamics”, Dokl. Akad. Nauk SSSR, 311:3 (1990),  549–552  mathnet  mathscinet  zmath; Dokl. Math., 35:3 (1990), 218–220
18. V. S. Kozyakin, “Observability of periodic modes that arise in the loss of stability of the equilibrium state of sampled-data systems”, Avtomat. i Telemekh., 1985, 9,  42–48  mathnet  mathscinet  zmath; Autom. Remote Control, 46 (1985), 1098–1104
19. V. S. Kozyakin, “On neglecting small terms in studies of nonlinear systems”, Avtomat. i Telemekh., 1984, 10,  38–43  mathnet  mathscinet  zmath; Autom. Remote Control, 45:10 (1984), 1275–1280
20. A. F. Kleptsyn, V. S. Kozyakin, M. Krasnosselsky, N. A. Kuznetsov, “On the effect of small desynchronization on stability of complex systems. III”, Avtomat. i Telemekh., 1984, 8,  63–67  mathnet  mathscinet  zmath; Autom. Remote Control, 45:8 (1984), 1014–1018
21. A. F. Kleptsyn, V. S. Kozyakin, M. A. Krasnosel'skii, N. A. Kuznetsov, “On the effect of small synchronization errors on stability of complex systems”, Avtomat. i Telemekh., 1984, 3,  42–47  mathnet  zmath; Autom. Remote Control, 45:3 (1984), 309–314
22. A. F. Kleptsyn, V. S. Kozyakin, M. A. Krasnosel'skii, N. A. Kuznetsov, “Stability of desynchronized systems”, Dokl. Akad. Nauk SSSR, 274:5 (1984),  1053–1056  mathnet  mathscinet  zmath
23. A. F. Kleptsyn, V. S. Kozyakin, M. Krasnosselsky, N. A. Kuznetsov, “On the effect of small synchronization errors on stability of complex systems. I”, Avtomat. i Telemekh., 1983, 7,  44–50  mathnet  zmath; Autom. Remote Control, 44:7 (1983), 861–867
24. A. A. Vladimirov, A. F. Kleptsyn, V. S. Kozyakin, M. A. Krasnosel'skii, E. A. Livshitz, A. V. Pokrovskii, “Vector hysteresis nonlinearities of the von Mises–Tresca type”, Dokl. Akad. Nauk SSSR, 257:3 (1981),  581–584  mathnet  mathscinet
25. V. S. Kozyakin, M. A. Krasnosel'skii, “The method of parameter functionalization in the problem of bifurcation points”, Dokl. Akad. Nauk SSSR, 254:5 (1980),  1061–1064  mathnet  mathscinet  zmath
26. V. S. Kozyakin, M. A. Krasnosel'skii, “Influence of small delays on dynamic behavior of nonlinear systems”, Avtomat. i Telemekh., 1979, 1,  5–8  mathnet  mathscinet  zmath; Autom. Remote Control, 40:1 (1979), 1–4
27. V. S. Kozyakin, M. A. Krasnosel'skii, “Some problems connected with the method of minimal residuals”, Zh. Vychisl. Mat. Mat. Fiz., 19:2 (1979),  508–510  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 19:2 (1979), 244–247
28. V. S. Kozyakin, “Subfurcation of periodic oscillations”, Dokl. Akad. Nauk SSSR, 232:1 (1977),  24–27  mathnet  mathscinet  zmath
29. V. S. Kozyakin, “The generation of periodic points from an equilibrium position”, Uspekhi Mat. Nauk, 32:4(196) (1977),  255–256  mathnet  mathscinet  zmath
30. V. S. Kozyakin, “The occurrence of subfurcation when there is loss of stability of the equilibrium state of a system of differential equations with lag”, Sibirsk. Mat. Zh., 18:3 (1977),  580–594  mathnet  mathscinet  zmath; Siberian Math. J., 18:3 (1977), 414–425  isi
31. R. R. Akhmerov, M. I. Kamenskii, V. S. Kozyakin, A. V. Sobolev, “Periodic solutions of systems of autonomous functional-differential equations of neutral type with small lag”, Differ. Uravn., 10:11 (1974),  1923–1931  mathnet  mathscinet  zmath
32. V. S. Kozyakin, M. A. Krasnosel'skii, A. V. Pokrovskii, “Vibrationally stable hysterons”, Dokl. Akad. Nauk SSSR, 206:4 (1972),  800–803  mathnet  mathscinet  zmath
33. V. S. Kozyakin, “The vibrostability of second order differential equations”, Uspekhi Mat. Nauk, 27:5(167) (1972),  241–242  mathnet  mathscinet  zmath
34. V. S. Kozyakin, “A functional equation”, Mat. Zametki, 9:2 (1971),  161–170  mathnet  mathscinet  zmath; Math. Notes, 9:2 (1971), 95–100

35. E. A. Asarin, I. A. Bakhtin, N. A. Bobylev, V. A. Bondarenko, V. Sh. Burd, E. A. Gorin, S. V. Emel'yanov, P. P. Zabreiko, L. A. Ivanov, V. S. Kozyakin, A. M. Krasnosel'skii, N. A. Kuznetsov, A. B. Kurzhanskii, A. Yu. Levin, È. M. Muhamadiev, A. I. Perov, Yu. V. Pokornyi, A. V. Pokrovskii, D. I. Rachinskii, V. V. Strygin, Ya. Z. Tsypkin, V. V. Chernorutski, “Memory of M. A. Krasnosel'skii”, Avtomat. i Telemekh., 1998, 2,  179–184  mathnet

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