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Kolesov Andrei Yurevich

Publications in Math-Net.Ru

  1. Annulus principle in the problem of the existence of an infinite-dimensional invariant torus

    Uspekhi Mat. Nauk, 81:1(487) (2026),  71–136
  2. On two different approaches to hyperbolicity definition

    Mat. Sb., 217:2 (2026),  34–70
  3. On a Method for Verifying Hyperbolicity

    Regul. Chaotic Dyn., 30:1 (2025),  45–56
  4. Integral networks of nonlinear oscillators

    TMF, 224:1 (2025),  42–62
  5. Dynamic self-organization in neural networks systems

    Zh. Vychisl. Mat. Mat. Fiz., 65:4 (2025),  574–589
  6. On a paradoxical property of the shift mapping on an infinite-dimensional tori

    Dokl. RAN. Math. Inf. Proc. Upr., 515 (2024),  28–33
  7. Multi-dimensional hyperbolic chaos

    Funktsional. Anal. i Prilozhen., 58:4 (2024),  3–19
  8. Cone criterion on an infinite-dimensional torus

    Izv. RAN. Ser. Mat., 88:6 (2024),  82–117
  9. A new approach to mathematical modeling of chemical synapses

    Izvestiya VUZ. Applied Nonlinear Dynamics, 32:3 (2024),  376–393
  10. Symmetric hyperbolic trap

    Mat. Zametki, 116:3 (2024),  372–387
  11. Dynamical systems on an infinite-dimensional torus: Fundamentals of hyperbolic theory

    Tr. Mosk. Mat. Obs., 84:1 (2023),  55–116
  12. Topologically Mixing Diffeomorphisms on the Infinite-Dimensional Torus

    Mat. Zametki, 113:6 (2023),  929–934
  13. Self-oscillatory processes in a discrete $RCL$-line with a tunnel diode

    TMF, 215:2 (2023),  207–224
  14. Релаксационные автоволны в математических моделях экологии

    Tr. Semim. im. I. G. Petrovskogo, 33 (2023),  83–143
  15. Hunt for chimeras in fully coupled networks of nonlinear oscillators

    Izvestiya VUZ. Applied Nonlinear Dynamics, 30:2 (2022),  152–175
  16. Hyperbolicity Criterion for Torus Endomorphisms

    Mat. Zametki, 111:1 (2022),  134–139
  17. Elements of hyperbolic theory on an infinite-dimensional torus

    Uspekhi Mat. Nauk, 77:3(465) (2022),  3–72
  18. A hyperbolicity criterion for a class of diffeomorphisms of an infinite-dimensional torus

    Mat. Sb., 213:2 (2022),  50–95
  19. Periodic two-cluster synchronization modes in fully coupled networks of nonlinear oscillators

    TMF, 212:2 (2022),  213–233
  20. Traveling waves in fully coupled networks of linear oscillators

    Zh. Vychisl. Mat. Mat. Fiz., 62:1 (2022),  71–89
  21. On a mathematical model of the repressilator

    Algebra i Analiz, 33:5 (2021),  80–124
  22. On some modifications of Arnold's cat map

    Dokl. RAN. Math. Inf. Proc. Upr., 500 (2021),  26–30
  23. On a class of Anosov diffeomorphisms on the infinite-dimensional torus

    Izv. RAN. Ser. Mat., 85:2 (2021),  3–59
  24. Periodic modes of group dominance in fully coupled neural networks

    Izvestiya VUZ. Applied Nonlinear Dynamics, 29:5 (2021),  775–798
  25. On the Existence and Stability of an Infinite-Dimensional Invariant Torus

    Mat. Zametki, 109:4 (2021),  508–528
  26. Expansive Endomorphisms on the Infinite-Dimensional Torus

    Funktsional. Anal. i Prilozhen., 54:4 (2020),  17–36
  27. Relaxation autowaves in a bi-local neuron model

    Tr. Mosk. Mat. Obs., 81:1 (2020),  41–85
  28. Solenoidal attractors of diffeomorphisms of annular sets

    Uspekhi Mat. Nauk, 75:2(452) (2020),  3–60
  29. On Some Sufficient Hyperbolicity Conditions

    Trudy Mat. Inst. Steklova, 308 (2020),  116–134
  30. Diffusion chaos and its invariant numerical characteristics

    TMF, 203:1 (2020),  10–25
  31. New approach to gene network modeling

    Model. Anal. Inform. Sist., 26:3 (2019),  365–404
  32. On the Hyperbolicity of Toral Endomorphisms

    Mat. Zametki, 105:2 (2019),  251–268
  33. A self-symmetric cycle in a system of two diffusely connected Hutchinson's equations

    Mat. Sb., 210:2 (2019),  24–74
  34. On a Mathematical Model of Biological Self-Organization

    Trudy Mat. Inst. Steklova, 304 (2019),  174–204
  35. Autowave processes in diffusion neuron systems

    Zh. Vychisl. Mat. Mat. Fiz., 59:9 (2019),  1495–1515
  36. An approach to modeling artificial gene networks

    TMF, 194:3 (2018),  547–568
  37. Quasi-stable structures in circular gene networks

    Zh. Vychisl. Mat. Mat. Fiz., 58:5 (2018),  682–704
  38. Many-circuit canard trajectories and their applications

    Izv. RAN. Ser. Mat., 81:4 (2017),  108–157
  39. Relaxation oscillations in a system of two pulsed synaptically coupled neurons

    Model. Anal. Inform. Sist., 24:1 (2017),  82–93
  40. Existence and Stability of the Relaxation Cycle in a Mathematical Repressilator Model

    Mat. Zametki, 101:1 (2017),  58–76
  41. Two-frequency self-oscillations in a FitzHugh–Nagumo neural network

    Zh. Vychisl. Mat. Mat. Fiz., 57:1 (2017),  94–110
  42. Periodic solutions of travelling-wave type in circular gene networks

    Izv. RAN. Ser. Mat., 80:3 (2016),  67–94
  43. The annulus principle in the existence problem for a hyperbolic strange attractor

    Mat. Sb., 207:4 (2016),  15–46
  44. Buffering in cyclic gene networks

    TMF, 187:3 (2016),  560–579
  45. Self-excited wave processes in chains of unidirectionally coupled impulse neurons

    Model. Anal. Inform. Sist., 22:3 (2015),  404–419
  46. Blue sky catastrophe in systems with non-classical relaxation oscillations

    Model. Anal. Inform. Sist., 22:1 (2015),  38–64
  47. Self-excited relaxation oscillations in networks of impulse neurons

    Uspekhi Mat. Nauk, 70:3(423) (2015),  3–76
  48. Blue sky catastrophe as applied to modeling of cardiac rhythms

    Zh. Vychisl. Mat. Mat. Fiz., 55:7 (2015),  1136–1155
  49. The buffer phenomenon in ring-like chains of unidirectionally connected generators

    Izv. RAN. Ser. Mat., 78:4 (2014),  73–108
  50. On the number of coexisting autowaves in the chain of coupled oscillators

    Model. Anal. Inform. Sist., 21:5 (2014),  162–180
  51. Non-Classical Relaxation Oscillations in Neurodynamics

    Model. Anal. Inform. Sist., 21:2 (2014),  71–89
  52. On One Means of Hard Excitation of Oscillations in Nonlinear Flutter Systems

    Model. Anal. Inform. Sist., 21:1 (2014),  32–44
  53. The theory of nonclassical relaxation oscillations in singularly perturbed delay systems

    Mat. Sb., 205:6 (2014),  21–86
  54. Autowave processes in continual chains of unidirectionally coupled oscillators

    Trudy Mat. Inst. Steklova, 285 (2014),  89–106
  55. Buffering effect in continuous chains of unidirectionally coupled generators

    TMF, 181:2 (2014),  254–275
  56. On a modification of the FitzHugh–Nagumo neuron model

    Zh. Vychisl. Mat. Mat. Fiz., 54:3 (2014),  430–449
  57. Relaxation self-oscillations in Hopfield networks with delay

    Izv. RAN. Ser. Mat., 77:2 (2013),  53–96
  58. The Quasi-Normal Form of a System of Three Unidirectionally Coupled Singularly Perturbed Equations with Two Delays

    Model. Anal. Inform. Sist., 20:5 (2013),  158–167
  59. Modeling the Bursting Effect in Neuron Systems

    Mat. Zametki, 93:5 (2013),  684–701
  60. Invariant tori for a class of nonlinear evolution equations

    Mat. Sb., 204:6 (2013),  47–92
  61. Periodic traveling-wave-type solutions in circular chains of unidirectionally coupled equations

    TMF, 175:1 (2013),  62–83
  62. Self-excited wave processes in chains of diffusion-linked delay equations

    Uspekhi Mat. Nauk, 67:2(404) (2012),  109–156
  63. Discrete autowaves in systems of delay differential–difference equations in ecology

    Trudy Mat. Inst. Steklova, 277 (2012),  101–143
  64. Discrete autowaves in neural systems

    Zh. Vychisl. Mat. Mat. Fiz., 52:5 (2012),  840–858
  65. Multifrequency self-oscillations in two-dimensional lattices of coupled oscillators

    Izv. RAN. Ser. Mat., 75:3 (2011),  97–126
  66. The theory of relaxation oscillations for Hutchinson's equation

    Mat. Sb., 202:6 (2011),  51–82
  67. Relaxation oscillations and diffusion chaos in the Belousov reaction

    Zh. Vychisl. Mat. Mat. Fiz., 51:8 (2011),  1400–1418
  68. Multifrequency self-oscillations in two-dimensional lattices of coupled oscillators

    Trudy Inst. Mat. i Mekh. UrO RAN, 16:5 (2010),  82–94
  69. Buffer phenomenon in the spatially one-dimensional Swift–Hohenberg equation

    Trudy Mat. Inst. Steklova, 268 (2010),  137–154
  70. A modification of Hutchinson's equation

    Zh. Vychisl. Mat. Mat. Fiz., 50:12 (2010),  2099–2112
  71. Finite-dimensional models of diffusion chaos

    Zh. Vychisl. Mat. Mat. Fiz., 50:5 (2010),  860–875
  72. On the definition of ‘chaos’

    Uspekhi Mat. Nauk, 64:4(388) (2009),  125–172
  73. The question of the realizability of the Landau scenario for the development of turbulence

    TMF, 158:2 (2009),  292–311
  74. Dynamic effects associated with spatial discretization of nonlinear wave equations

    Zh. Vychisl. Mat. Mat. Fiz., 49:10 (2009),  1812–1826
  75. Extremal dynamics of the generalized Hutchinson equation

    Zh. Vychisl. Mat. Mat. Fiz., 49:1 (2009),  76–89
  76. Mathematical aspects of the theory of development of turbulence in the sense of Landau

    Uspekhi Mat. Nauk, 63:2(380) (2008),  21–84
  77. Resonance Dynamics of Nonlinear Flutter Systems

    Trudy Mat. Inst. Steklova, 261 (2008),  154–175
  78. The Buffer Phenomenon in One-Dimensional Piecewise Linear Mapping in Radiophysics

    Mat. Zametki, 81:4 (2007),  507–514
  79. The problem of birth of autowaves in parabolic systems with small diffusion

    Mat. Sb., 198:11 (2007),  67–106
  80. New Methods for Proving the Existence and Stability of Periodic Solutions in Singularly Perturbed Delay Systems

    Trudy Mat. Inst. Steklova, 259 (2007),  106–133
  81. Attractors of the Sine-Gordon Equation in the Field of a Quasiperiodic External Force

    Trudy Mat. Inst. Steklova, 256 (2007),  219–236
  82. Autowave processes in a long line without distortions

    Differ. Uravn., 42:2 (2006),  239–244
  83. Smoothing the discontinuous oscillations in the mathematical model of an oscillator with distributed parameters

    Izv. RAN. Ser. Mat., 70:6 (2006),  129–152
  84. The buffer property in a non-classical hyperbolic boundary-value problem from radiophysics

    Mat. Sb., 197:6 (2006),  63–96
  85. Buffer phenomenon in systems close to two-dimensional Hamiltonian ones

    Trudy Inst. Mat. i Mekh. UrO RAN, 12:1 (2006),  109–141
  86. The nature of the bufferness phenomenon in weakly dissipative systems

    TMF, 146:3 (2006),  447–466
  87. Chaos phenomena in a circle of three unidirectionally connected oscillators

    Zh. Vychisl. Mat. Mat. Fiz., 46:10 (2006),  1809–1821
  88. Buffer phenomenon in systems with one and a half degrees of freedom

    Zh. Vychisl. Mat. Mat. Fiz., 46:9 (2006),  1582–1593
  89. The Dynamic Renormalization Method for Finding the Maximum Lyapunov Exponent of a Chaotic Attractor

    Differ. Uravn., 41:2 (2005),  268–273
  90. Chaotic buffering property in chains of coupled oscillators

    Differ. Uravn., 41:1 (2005),  41–49
  91. Buffer Phenomenon in Nonlinear Physics

    Trudy Mat. Inst. Steklova, 250 (2005),  112–182
  92. The mechanism of hard excitation of self-oscillations in the case of the resonance 1:2

    Zh. Vychisl. Mat. Mat. Fiz., 45:11 (2005),  2000–2016
  93. Attractors of Singularly Perturbed Parabolic Systems of First Degree of Nonroughness in a Plane Domain

    Mat. Zametki, 75:5 (2004),  663–669
  94. Optical Buffering and Mechanisms for Its Occurrence

    TMF, 140:1 (2004),  14–28
  95. On the theoretical explanation of the diffusion buffer phenomenon

    Zh. Vychisl. Mat. Mat. Fiz., 44:11 (2004),  2020–2040
  96. Invariant Tori of a Class of Point Transformations: Preservation of an Invariant Torus Under Perturbations

    Differ. Uravn., 39:6 (2003),  738–753
  97. Invariant Tori of a Class of Point Mappings: The Annulus Principle

    Differ. Uravn., 39:5 (2003),  584–601
  98. On-Off Intermittency in Relaxation Systems

    Differ. Uravn., 39:1 (2003),  35–44
  99. The existence of countably many stable cycles for a generalized cubic Schrödinger equation in a planar domain

    Izv. RAN. Ser. Mat., 67:6 (2003),  137–168
  100. Two-Frequency Autowave Processes in the Complex Ginzburg–Landau Equation

    TMF, 134:3 (2003),  353–373
  101. Attractors of Hard Turbulence Type in Relaxation Systems

    Differ. Uravn., 38:12 (2002),  1596–1605
  102. The Buffer Phenomenon in the Van Der Pol Oscillator with Delay

    Differ. Uravn., 38:2 (2002),  165–176
  103. Multifrequency parametric resonance in a non-linear wave equation

    Izv. RAN. Ser. Mat., 66:6 (2002),  49–64
  104. The “Duck Survival” Problem in Three-Dimensional Singularly Perturbed Systems with Two Slow Variables

    Mat. Zametki, 71:6 (2002),  818–831
  105. Impact of quadratic non-linearity on the dynamics of periodic solutions of a wave equation

    Mat. Sb., 193:1 (2002),  93–118
  106. The buffer phenomenon in a mathematical model of the van der Pol self-oscillator with distributed parameters

    Izv. RAN. Ser. Mat., 65:3 (2001),  67–84
  107. The Parametric Buffer Phenomenon for a Singularly Perturbed Telegraph Equation with a Pendulum Nonlinearity

    Mat. Zametki, 69:6 (2001),  866–875
  108. The Bufferness Phenomenon in the RCLG Seft-excited Oscillator: Theoretical Analysis and Experiment Results

    Trudy Mat. Inst. Steklova, 233 (2001),  153–207
  109. Existence of solutions with turning points for nonlinear singularly perturbed boundary value problems

    Mat. Zametki, 67:4 (2000),  520–524
  110. The buffer property in resonance systems of non-linear hyperbolic equations

    Uspekhi Mat. Nauk, 55:2(332) (2000),  95–120
  111. Parametric excitation of high-mode oscillations for a non-linear telegraph equation

    Mat. Sb., 191:8 (2000),  45–68
  112. Characteristic features of the dynamics of the Ginzburg–Landau equation in a plane domain

    TMF, 125:2 (2000),  205–220
  113. Solvability of a nonclassical parabolic problem arising in radiophysics

    Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2000, no. 5,  12–19
  114. Asymptotic investigation of a hyperbolic boundary value problem in radio physics

    Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2000, no. 1,  21–26
  115. “Duck hunting” in the study of singularly perturbed boundary value problems

    Differ. Uravn., 35:10 (1999),  1356–1365
  116. Specifity of the auto oscillatory processes in resonance hyperbolic systems

    Fundam. Prikl. Mat., 5:2 (1999),  437–473
  117. Asymptotic theory of oscillations in the Vitt system

    Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 67 (1999),  5–68
  118. The “Buridan's Ass” problem in relaxation systems with one slow variable

    Mat. Zametki, 65:1 (1999),  153–156
  119. Solution to Singularly Perturbed Boundary Value Problems by the Duck Hunting Method

    Trudy Mat. Inst. Steklova, 224 (1999),  187–207
  120. Auto-oscillations in an RCLG-line with small distortion

    Differ. Uravn., 34:11 (1998),  1559–1561
  121. The diffusion-buffer phenomenon in a mathematical model of biology

    Izv. RAN. Ser. Mat., 62:5 (1998),  135–164
  122. Diffusion instability of a uniform cycle bifurcating from a separatrix loop

    Mat. Zametki, 63:5 (1998),  697–708
  123. Asymptotic Methods of Investigation of Periodic Solutions of Nonlinear Hyperbolic Equations

    Trudy Mat. Inst. Steklova, 222 (1998),  3–191
  124. External action as a method for the regularization of discontinuous oscillations in a nonlinear telegraph equation

    Trudy Mat. Inst. Steklova, 220 (1998),  157–172
  125. Existence and stability of rapidly oscillating cycles for the nonlinear telegraph equation

    Zh. Vychisl. Mat. Mat. Fiz., 38:8 (1998),  1287–1300
  126. Theoretical and experimental analysis of the buffer phenomenon in a long line with a tunnel diode

    Differ. Uravn., 33:5 (1997),  638–645
  127. Chaos of 'split torus' type in three-dimensional relaxation systems

    Mat. Sb., 188:11 (1997),  3–18
  128. Relay with delay and its $C^1$-approximation

    Trudy Mat. Inst. Steklova, 216 (1997),  126–153
  129. On $C^1$-approximation of solutions of systems of differential equations with piecewise-continuous right-hand sides

    Dokl. Akad. Nauk, 349:2 (1996),  162–164
  130. Duck cycles of three-dimensional relaxation systems with one fast and two slow variables

    Differ. Uravn., 32:2 (1996),  180–184
  131. On a certain model hyperbolic equation arising in radiophysics

    Mat. Model., 8:1 (1996),  93–102
  132. A four-dimensional analog of Lyapunov's classical stability problem

    Mat. Zametki, 60:4 (1996),  612–615
  133. Bifurcation of periodic motions under $1:1$ Resonance with Jordan blocks

    Mat. Zametki, 60:3 (1996),  450–451
  134. Relaxation cycles of a nonlinear wave equation that smoothly depends on the parameters

    Dokl. Akad. Nauk, 341:2 (1995),  158–160
  135. Construction of periodic solutions of a Boussinnesq type equation using the method of quasi-normal forms

    Fundam. Prikl. Mat., 1:1 (1995),  207–220
  136. Existence of countably many stable cycles in media with dispersion

    Izv. RAN. Ser. Mat., 59:3 (1995),  141–158
  137. The buffering phenomenon in a resonance hyperbolic boundary-value problem in radiophysics

    Mat. Sb., 186:7 (1995),  77–96
  138. On the existence and stability of a two-dimensional relaxational torus

    Mat. Zametki, 56:6 (1994),  40–47
  139. Application of techniques of relaxation oscillations to a system of differential-difference equations from ecology

    Mat. Sb., 185:1 (1994),  95–106
  140. Relaxational oscillations in mathematical models of ecology

    Trudy Mat. Inst. Steklov., 199 (1993),  3–124
  141. Relaxation cycles of differential-difference equations

    Izv. RAN. Ser. Mat., 56:4 (1992),  790–812
  142. Stability of the autooscillations of the telegraph equation, bifurcating from an equilibrium state

    Mat. Zametki, 51:2 (1992),  59–65
  143. Relaxation cycles in systems with delay

    Mat. Sb., 183:8 (1992),  141–159
  144. Parametric oscillations of solutions to the telegraph equation with moderately small diffusion

    Sibirsk. Mat. Zh., 33:6 (1992),  79–86
  145. A new class of relaxation systems in general position

    Dokl. Akad. Nauk SSSR, 316:3 (1991),  546–549
  146. Specific relaxation cycles of systems of Lotka–Volterra type

    Izv. Akad. Nauk SSSR Ser. Mat., 55:3 (1991),  515–536
  147. Self-oscillations of singularly perturbed parabolic systems of first degree of nonroughness

    Mat. Zametki, 49:5 (1991),  62–69
  148. Existence and stability of relaxation travelling waves for the non-linear telegraph equation with a small diffusion

    Uspekhi Mat. Nauk, 46:2(278) (1991),  221–222
  149. On the mechanism of destruction of invariant torus of Van-der Pole relaxation system with harmonic influence on the slow variable

    Trudy Mat. Inst. Steklov., 200 (1991),  197–204
  150. Asymptotical theory of relaxational oscillations

    Trudy Mat. Inst. Steklov., 197 (1991),  3–84
  151. Bifurcation of self-induced oscillations of a singularly perturbed wave equation

    Dokl. Akad. Nauk SSSR, 315:2 (1990),  281–283
  152. The Pontryagin delay phenomenon and stable ducktrajectories for multidimensional relaxation systems with one slow variable

    Mat. Sb., 181:5 (1990),  579–588
  153. The Bogolyubov–Mitropol'skii reduction principle in the problem of parametric excitation of autowaves

    Dokl. Akad. Nauk SSSR, 307:4 (1989),  837–840
  154. Relaxation parabolic systems

    Dokl. Akad. Nauk SSSR, 306:6 (1989),  1297–1300
  155. A mixing attractor in relaxation systems

    Dokl. Akad. Nauk SSSR, 306:1 (1989),  38–40
  156. A problem of Pontryagin

    Differ. Uravn., 25:11 (1989),  1888–1891
  157. The structure of a neighborhood of a homogeneous cycle in a medium with diffusion

    Izv. Akad. Nauk SSSR Ser. Mat., 53:2 (1989),  345–362
  158. Chaos phenomena in three-dimensional relaxation systems

    Mat. Zametki, 46:2 (1989),  153–155
  159. On the instability of duck-cycles arising during the passage of an equilibrium of a multidimensional relaxation system through the disruption manifold

    Uspekhi Mat. Nauk, 44:5(269) (1989),  165–166
  160. Existence and stability of the relaxation torus

    Uspekhi Mat. Nauk, 44:3(267) (1989),  161–162
  161. Duck trajectories of relaxation systems connected with violation of the normal switching conditions

    Mat. Sb., 180:10 (1989),  1428–1438
  162. A criterion for the stability of traveling waves of parabolic systems with small diffusion

    Sibirsk. Mat. Zh., 30:3 (1989),  175–179
  163. Multidimensional relaxation oscillations in media with diffusion

    Dokl. Akad. Nauk SSSR, 302:6 (1988),  1312–1315
  164. Description of the phase instability of a system of harmonic oscillators that are weakly connected by diffusion

    Dokl. Akad. Nauk SSSR, 300:4 (1988),  831–835
  165. Construction of the normal form in a neighborhood of a cycle by means of the Krylov–Bogolyubov–Mitropol'skiǐ asymptotic method

    Differ. Uravn., 24:5 (1988),  891–894
  166. Properties of a certain linear system connected with the stability of the relaxation cycle in media with diffusion

    Uspekhi Mat. Nauk, 43:3(261) (1988),  185–186
  167. A relaxation system in the neighbourhood of a disruption point: reduction to the regular case

    Uspekhi Mat. Nauk, 43:2(260) (1988),  141–142
  168. Asymptotics of relaxation oscilations

    Mat. Sb. (N.S.), 137(179):1(9) (1988),  3–18
  169. Stability of relaxation auto-oscillations in systems with diffusion

    Dokl. Akad. Nauk SSSR, 294:3 (1987),  575–578
  170. Asymptotic integration of the variational system of a multidimensional relaxation cycle. II

    Differ. Uravn., 23:12 (1987),  2036–2047
  171. Asymptotic integration of the variational system of a multidimensional relaxation cycle. I

    Differ. Uravn., 23:11 (1987),  1881–1889

  172. In memory of Evgenii Frolovich Mishchenko

    Trudy Mat. Inst. Steklova, 271 (2010),  7–8

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