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Publications in Math-Net.Ru
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Релаксационные автоволны в математических моделях экологии
Tr. Semim. im. I. G. Petrovskogo, 33 (2023), 83–143
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On a mathematical model of the repressilator
Algebra i Analiz, 33:5 (2021), 80–124
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On a class of Anosov diffeomorphisms on the infinite-dimensional torus
Izv. RAN. Ser. Mat., 85:2 (2021), 3–59
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On the Existence and Stability of an Infinite-Dimensional Invariant Torus
Mat. Zametki, 109:4 (2021), 508–528
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Expansive Endomorphisms on the Infinite-Dimensional Torus
Funktsional. Anal. i Prilozhen., 54:4 (2020), 17–36
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Relaxation autowaves in a bi-local neuron model
Tr. Mosk. Mat. Obs., 81:1 (2020), 41–85
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Solenoidal attractors of diffeomorphisms of annular sets
Uspekhi Mat. Nauk, 75:2(452) (2020), 3–60
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On Some Sufficient Hyperbolicity Conditions
Trudy Mat. Inst. Steklova, 308 (2020), 116–134
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Diffusion chaos and its invariant numerical characteristics
TMF, 203:1 (2020), 10–25
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New approach to gene network modeling
Model. Anal. Inform. Sist., 26:3 (2019), 365–404
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On the Hyperbolicity of Toral Endomorphisms
Mat. Zametki, 105:2 (2019), 251–268
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A self-symmetric cycle in a system of two diffusely connected Hutchinson's equations
Mat. Sb., 210:2 (2019), 24–74
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On a Mathematical Model of Biological Self-Organization
Trudy Mat. Inst. Steklova, 304 (2019), 174–204
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Autowave processes in diffusion neuron systems
Zh. Vychisl. Mat. Mat. Fiz., 59:9 (2019), 1495–1515
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An approach to modeling artificial gene networks
TMF, 194:3 (2018), 547–568
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Quasi-stable structures in circular gene networks
Zh. Vychisl. Mat. Mat. Fiz., 58:5 (2018), 682–704
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Many-circuit canard trajectories and their applications
Izv. RAN. Ser. Mat., 81:4 (2017), 108–157
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Existence and Stability of the Relaxation Cycle in a Mathematical Repressilator Model
Mat. Zametki, 101:1 (2017), 58–76
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Two-frequency self-oscillations in a FitzHugh–Nagumo neural network
Zh. Vychisl. Mat. Mat. Fiz., 57:1 (2017), 94–110
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Periodic solutions of travelling-wave type in circular gene networks
Izv. RAN. Ser. Mat., 80:3 (2016), 67–94
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The annulus principle in the existence problem for a hyperbolic strange attractor
Mat. Sb., 207:4 (2016), 15–46
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Buffering in cyclic gene networks
TMF, 187:3 (2016), 560–579
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Self-excited wave processes in chains of unidirectionally coupled impulse neurons
Model. Anal. Inform. Sist., 22:3 (2015), 404–419
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Blue sky catastrophe in systems with non-classical relaxation oscillations
Model. Anal. Inform. Sist., 22:1 (2015), 38–64
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Математический юбилей трёхликого сборника
Mat. Pros., Ser. 3, 19 (2015), 7–23
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Self-excited relaxation oscillations in networks of impulse neurons
Uspekhi Mat. Nauk, 70:3(423) (2015), 3–76
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Blue sky catastrophe as applied to modeling of cardiac rhythms
Zh. Vychisl. Mat. Mat. Fiz., 55:7 (2015), 1136–1155
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The buffer phenomenon in ring-like chains of unidirectionally connected generators
Izv. RAN. Ser. Mat., 78:4 (2014), 73–108
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Non-Classical Relaxation Oscillations in Neurodynamics
Model. Anal. Inform. Sist., 21:2 (2014), 71–89
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On One Means of Hard Excitation of Oscillations in Nonlinear Flutter Systems
Model. Anal. Inform. Sist., 21:1 (2014), 32–44
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The theory of nonclassical relaxation oscillations in singularly perturbed delay systems
Mat. Sb., 205:6 (2014), 21–86
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Autowave processes in continual chains of unidirectionally coupled oscillators
Trudy Mat. Inst. Steklova, 285 (2014), 89–106
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Buffering effect in continuous chains of unidirectionally coupled generators
TMF, 181:2 (2014), 254–275
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Scientific heritage of Vladimir Mikhailovich Millionshchikov
Tr. Semim. im. I. G. Petrovskogo, 30 (2014), 5–41
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On a modification of the FitzHugh–Nagumo neuron model
Zh. Vychisl. Mat. Mat. Fiz., 54:3 (2014), 430–449
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Relaxation self-oscillations in Hopfield networks with delay
Izv. RAN. Ser. Mat., 77:2 (2013), 53–96
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Modeling the Bursting Effect in Neuron Systems
Mat. Zametki, 93:5 (2013), 684–701
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Invariant tori for a class of nonlinear evolution equations
Mat. Sb., 204:6 (2013), 47–92
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Periodic traveling-wave-type solutions in circular chains of unidirectionally coupled equations
TMF, 175:1 (2013), 62–83
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Self-excited wave processes in chains of diffusion-linked delay equations
Uspekhi Mat. Nauk, 67:2(404) (2012), 109–156
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Discrete autowaves in systems of delay differential–difference equations in ecology
Trudy Mat. Inst. Steklova, 277 (2012), 101–143
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Discrete autowaves in neural systems
Zh. Vychisl. Mat. Mat. Fiz., 52:5 (2012), 840–858
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Multifrequency self-oscillations in two-dimensional lattices of coupled oscillators
Izv. RAN. Ser. Mat., 75:3 (2011), 97–126
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The theory of relaxation oscillations for Hutchinson's equation
Mat. Sb., 202:6 (2011), 51–82
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Relaxation oscillations and diffusion chaos in the Belousov reaction
Zh. Vychisl. Mat. Mat. Fiz., 51:8 (2011), 1400–1418
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Multifrequency self-oscillations in two-dimensional lattices of coupled oscillators
Trudy Inst. Mat. i Mekh. UrO RAN, 16:5 (2010), 82–94
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Buffer phenomenon in the spatially one-dimensional Swift–Hohenberg equation
Trudy Mat. Inst. Steklova, 268 (2010), 137–154
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The buffer phenomenon in mathematical models of natural sciences
Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2010, no. 3, 58–63
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A modification of Hutchinson's equation
Zh. Vychisl. Mat. Mat. Fiz., 50:12 (2010), 2099–2112
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Finite-dimensional models of diffusion chaos
Zh. Vychisl. Mat. Mat. Fiz., 50:5 (2010), 860–875
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On the definition of ‘chaos’
Uspekhi Mat. Nauk, 64:4(388) (2009), 125–172
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The question of the realizability of the Landau scenario for the development of turbulence
TMF, 158:2 (2009), 292–311
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Dynamic effects associated with spatial discretization of nonlinear wave equations
Zh. Vychisl. Mat. Mat. Fiz., 49:10 (2009), 1812–1826
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Extremal dynamics of the generalized Hutchinson equation
Zh. Vychisl. Mat. Mat. Fiz., 49:1 (2009), 76–89
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Mathematical aspects of the theory of development of turbulence in the sense of Landau
Uspekhi Mat. Nauk, 63:2(380) (2008), 21–84
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Resonance Dynamics of Nonlinear Flutter Systems
Trudy Mat. Inst. Steklova, 261 (2008), 154–175
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The Buffer Phenomenon in One-Dimensional Piecewise Linear Mapping in Radiophysics
Mat. Zametki, 81:4 (2007), 507–514
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The problem of birth of autowaves in parabolic
systems with small diffusion
Mat. Sb., 198:11 (2007), 67–106
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New Methods for Proving the Existence and Stability of Periodic Solutions in Singularly Perturbed Delay Systems
Trudy Mat. Inst. Steklova, 259 (2007), 106–133
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Attractors of the Sine-Gordon Equation in the Field of a Quasiperiodic External Force
Trudy Mat. Inst. Steklova, 256 (2007), 219–236
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Autowave processes in a long line without distortions
Differ. Uravn., 42:2 (2006), 239–244
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Smoothing the discontinuous oscillations in the mathematical model of an oscillator with distributed parameters
Izv. RAN. Ser. Mat., 70:6 (2006), 129–152
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The buffer property in a non-classical hyperbolic
boundary-value problem from radiophysics
Mat. Sb., 197:6 (2006), 63–96
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Buffer phenomenon in systems close to two-dimensional Hamiltonian ones
Trudy Inst. Mat. i Mekh. UrO RAN, 12:1 (2006), 109–141
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The nature of the bufferness phenomenon in weakly dissipative systems
TMF, 146:3 (2006), 447–466
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Chaos phenomena in a circle of three unidirectionally connected oscillators
Zh. Vychisl. Mat. Mat. Fiz., 46:10 (2006), 1809–1821
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Buffer phenomenon in systems with one and a half degrees of freedom
Zh. Vychisl. Mat. Mat. Fiz., 46:9 (2006), 1582–1593
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The Dynamic Renormalization Method for Finding the Maximum Lyapunov Exponent of a Chaotic Attractor
Differ. Uravn., 41:2 (2005), 268–273
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Chaotic buffering property in chains of coupled oscillators
Differ. Uravn., 41:1 (2005), 41–49
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Buffer Phenomenon in Nonlinear Physics
Trudy Mat. Inst. Steklova, 250 (2005), 112–182
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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
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Attractors of Singularly Perturbed Parabolic Systems of First Degree of Nonroughness in a Plane Domain
Mat. Zametki, 75:5 (2004), 663–669
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Optical Buffering and Mechanisms for Its Occurrence
TMF, 140:1 (2004), 14–28
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On the theoretical explanation of the diffusion buffer phenomenon
Zh. Vychisl. Mat. Mat. Fiz., 44:11 (2004), 2020–2040
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Invariant Tori of a Class of Point Transformations: Preservation of an Invariant Torus Under Perturbations
Differ. Uravn., 39:6 (2003), 738–753
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Invariant Tori of a Class of Point Mappings: The Annulus Principle
Differ. Uravn., 39:5 (2003), 584–601
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On-Off Intermittency in Relaxation Systems
Differ. Uravn., 39:1 (2003), 35–44
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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
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Two-Frequency Autowave Processes in the Complex Ginzburg–Landau Equation
TMF, 134:3 (2003), 353–373
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Attractors of Hard Turbulence Type in Relaxation Systems
Differ. Uravn., 38:12 (2002), 1596–1605
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The Buffer Phenomenon in the Van Der Pol Oscillator with Delay
Differ. Uravn., 38:2 (2002), 165–176
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Multifrequency parametric resonance in a non-linear wave equation
Izv. RAN. Ser. Mat., 66:6 (2002), 49–64
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The “Duck Survival” Problem in Three-Dimensional Singularly Perturbed Systems with Two Slow Variables
Mat. Zametki, 71:6 (2002), 818–831
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Impact of quadratic non-linearity on the dynamics
of periodic solutions of a wave equation
Mat. Sb., 193:1 (2002), 93–118
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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
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The Parametric Buffer Phenomenon for a Singularly Perturbed Telegraph Equation with a Pendulum Nonlinearity
Mat. Zametki, 69:6 (2001), 866–875
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The Bufferness Phenomenon in the RCLG Seft-excited Oscillator: Theoretical Analysis and Experiment Results
Trudy Mat. Inst. Steklova, 233 (2001), 153–207
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Existence of solutions with turning points for nonlinear singularly perturbed boundary value problems
Mat. Zametki, 67:4 (2000), 520–524
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The buffer property in resonance systems of non-linear hyperbolic equations
Uspekhi Mat. Nauk, 55:2(332) (2000), 95–120
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Parametric excitation of high-mode oscillations for a non-linear telegraph equation
Mat. Sb., 191:8 (2000), 45–68
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Characteristic features of the dynamics of the Ginzburg–Landau equation in a plane domain
TMF, 125:2 (2000), 205–220
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Solvability of a nonclassical parabolic problem arising in radiophysics
Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2000, no. 5, 12–19
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Asymptotic investigation of a hyperbolic boundary value problem in radio physics
Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2000, no. 1, 21–26
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“Duck hunting” in the study of singularly perturbed boundary value problems
Differ. Uravn., 35:10 (1999), 1356–1365
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Specifity of the auto oscillatory processes in resonance hyperbolic systems
Fundam. Prikl. Mat., 5:2 (1999), 437–473
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Asymptotic theory of oscillations in the Vitt system
Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 67 (1999), 5–68
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The “Buridan's Ass” problem in relaxation systems with one slow variable
Mat. Zametki, 65:1 (1999), 153–156
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Solution to Singularly Perturbed Boundary Value Problems by the Duck Hunting Method
Trudy Mat. Inst. Steklova, 224 (1999), 187–207
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Auto-oscillations in an RCLG-line with small distortion
Differ. Uravn., 34:11 (1998), 1559–1561
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Differential equations with degenerate coefficient by order derivative
Fundam. Prikl. Mat., 4:3 (1998), 1063–1095
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The diffusion-buffer phenomenon in a mathematical model of biology
Izv. RAN. Ser. Mat., 62:5 (1998), 135–164
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Asymptotic Methods of Investigation of Periodic Solutions of Nonlinear Hyperbolic Equations
Trudy Mat. Inst. Steklova, 222 (1998), 3–191
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External action as a method for the regularization of discontinuous oscillations in a nonlinear telegraph equation
Trudy Mat. Inst. Steklova, 220 (1998), 157–172
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Existence and stability of rapidly oscillating cycles for the nonlinear telegraph equation
Zh. Vychisl. Mat. Mat. Fiz., 38:8 (1998), 1287–1300
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Theoretical and experimental analysis of the buffer phenomenon in a long line with a tunnel diode
Differ. Uravn., 33:5 (1997), 638–645
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Асимптотическое решение бисингулярных обыкновенных дифференциальных уравнений
Matem. Mod., 9:10 (1997), 33
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Внутренний слой в краевых задачах для сингулярно возмущенных обыкновенных дифференциальных уравнений с разрывной правой частью
Matem. Mod., 9:10 (1997), 31–32
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Chaos of 'split torus' type in three-dimensional relaxation systems
Mat. Sb., 188:11 (1997), 3–18
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Relay with delay and its $C^1$-approximation
Trudy Mat. Inst. Steklova, 216 (1997), 126–153
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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
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Duck cycles of three-dimensional relaxation systems with one fast and two slow variables
Differ. Uravn., 32:2 (1996), 180–184
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Perturbation of linear swift processes
Fundam. Prikl. Mat., 1:3 (1995), 649–660
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Construction of periodic solutions of a Boussinnesq type equation using the method of quasi-normal forms
Fundam. Prikl. Mat., 1:1 (1995), 207–220
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Duck cycles of differential-difference equations
Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1995, no. 1, 12–17
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The method of barrier functions and asymptotic solutions of
singularly perturbed boundary value problems
Dokl. Akad. Nauk, 332:3 (1993), 294–296
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A mixing attractor in relaxation systems
Dokl. Akad. Nauk SSSR, 306:1 (1989), 38–40
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Asymptotic representations of solutions of some singularly
perturbed boundary value problems
Dokl. Akad. Nauk SSSR, 304:4 (1989), 777–780
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Chaos phenomena in three-dimensional relaxation systems
Mat. Zametki, 46:2 (1989), 153–155
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Multidimensional relaxation oscillations in media with diffusion
Dokl. Akad. Nauk SSSR, 302:6 (1988), 1312–1315
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A relaxation system in the neighbourhood of a disruption point: reduction to the regular case
Uspekhi Mat. Nauk, 43:2(260) (1988), 141–142
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Asymptotic integration of the variational system of a multidimensional relaxation cycle. II
Differ. Uravn., 23:12 (1987), 2036–2047
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Asymptotic integration of the variational system of a multidimensional relaxation cycle. I
Differ. Uravn., 23:11 (1987), 1881–1889
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Bifurcation of self-oscillations of nonlinear parabolic equations with small diffusion
Mat. Sb. (N.S.), 130(172):4(8) (1986), 488–499
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Asymptotic theory of two-dimensional relaxation self-oscillating system
Mat. Zametki, 37:1 (1985), 125–136
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Singularly perturbed problems with a minimal pulse
Differ. Uravn., 19:2 (1983), 259–269
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On some special functions and constants arising in the theory of relaxation oscillations
Dokl. Akad. Nauk SSSR, 261:6 (1981), 1292–1296
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Differentiability of the support function of Pontryagin's alternating integral
Mat. Zametki, 30:6 (1981), 865–870
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The nonlinear controlled sampled-data system. II. Dependence of the solution on the initial state and parameters
Differ. Uravn., 16:2 (1980), 208–213
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The nonlinear controlled sampled-data system. I. Effect of certain perturbations
Differ. Uravn., 15:11 (1979), 1933–1939
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Distribution of Ljapunov exponents in linear systems with periodic coefficients that are nearly constant in the mean
Differ. Uravn., 14:9 (1978), 1710–1714
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A method based on turning solutions in the stabilization problem for linear dynamic systems with unstable equilibrium states
Avtomat. i Telemekh., 1975, no. 12, 18–26
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The local section method for systems with refraction of trajectories
Dokl. Akad. Nauk SSSR, 202:3 (1972), 535–538
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Some remarks on differential equations of the form $y^{''}+a_0(x)y=\varphi(x)y^\alpha$
Differ. Uravn., 8:11 (1972), 2076–2079
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Asymptotic calculation of nearly discontinuous solutions of a second-order system of differential equations
Dokl. Akad. Nauk SSSR, 145:1 (1962), 38–40
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Чертеж в геометрической задаче
Kvant, 2020, no. 11-12, 25–30
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Vasilii Vasilievich Zhikov
Tr. Semim. im. I. G. Petrovskogo, 32 (2019), 5–7
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Anniversary of Professor M. V. Shamolin
Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 134 (2017), 3–5
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Logics and School
Math. Ed., 2016, no. 1(77), 2–5
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In memory of Evgenii Leonidovich Tonkov (27.06.1940–28.09.2014)
Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, no. 4, 146–154
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Evgenii Frolovich Mishchenko (on the 90th anniversary of his birth)
Uspekhi Mat. Nauk, 67:2(404) (2012), 193–207
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Vladimir Alexandrovich Kondratiev. July 2, 1935 – March 11, 2010
CMFD, 39 (2011), 5–10
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Традиции математической олимпиады в Грузии
Mat. Pros., Ser. 3, 15 (2011), 204–205
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Olga Arsenjevna Oleinik
Tr. Semim. im. I. G. Petrovskogo, 28 (2011), 5–7
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Nikolai Alekseevich Izobov (A tribute in honor of his 70th birthday)
Differ. Uravn., 46:1 (2010), 3–8
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Какой будет школьная математика в 2050 году?
Math. Ed., 2010, no. 2(54), 2–7
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In memory of Evgenii Frolovich Mishchenko
Trudy Mat. Inst. Steklova, 271 (2010), 7–8
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To memory of Vladimir Mikhailovich Millionshchikov
Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2010, no. 2, 71–72
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Vladimir Alexandrovich Kondratiev on the 70th anniversary of his birth
Tr. Semim. im. I. G. Petrovskogo, 26 (2007), 5–28
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Vladimir Aleksandrovich Kondrat'ev (A Tribute in Honor of His 70th Birthday)
Differ. Uravn., 41:7 (2005), 867–873
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Sergei Konstantinovich Korovin (A Tribute in Honor of His Sixtieth Birthday)
Differ. Uravn., 41:5 (2005), 579–588
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Vladimir Aleksandrovich Kondrat'ev
Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2005, no. 5, 77–79
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Mikhail Tikhonovich Terekhin (a Tribute in Honor of His Seventieth Birthday)
Differ. Uravn., 40:1 (2004), 3–4
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Nikolaǐ Antonovich Bobylev
Differ. Uravn., 39:4 (2003), 570–572
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Ol'ga Arsen'evna Oleinik (obituary)
Uspekhi Mat. Nauk, 58:1(349) (2003), 165–174
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Arlen Mikhailovich Il'in (on the occasion of the 70th anniversary)
Trudy Inst. Mat. i Mekh. UrO RAN, 9:1 (2003), 3–9
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Arlen Mikhailovich Il'in (A tribute in honor of his 70th birthday)
Differ. Uravn., 38:8 (2002), 1011–1016
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N. V. Azbelev (A tribute on the occasion of his 80th birthday)
Differ. Uravn., 38:7 (2002), 867–869
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Viktor Aleksandrovich Pliss (A tribute in honor of his seventieth birthday)
Differ. Uravn., 38:2 (2002), 147–154
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Yulii Vital'evich Pokornyi (on his 60th birthday)
Uspekhi Mat. Nauk, 56:1(337) (2001), 199–200
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Nikolai Alekseevich Izobov
Differ. Uravn., 36:1 (2000), 3–11
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Anatolii Sergeevich Kalashnikov (obituary)
Uspekhi Mat. Nauk, 55:5(335) (2000), 161–168
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Vladimir Mikhaǐlovich Millionshchikov (on the occasion of his sixtieth birthday)
Differ. Uravn., 35:10 (1999), 1299–1312
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О Соросовском Образовательном Журнале
Differ. Uravn., 35:5 (1999), 715–716
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Феликс Клейн и его эрлангенская программа
Mat. Pros., Ser. 3, 3 (1999), 49–55
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Valentin Fedorovich Butuzov (on his 60th birthday)
Uspekhi Mat. Nauk, 54:6(330) (1999), 179–181
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Alekseǐ Fedorovich Filippov (on the occasion of his 75th anniversary)
Differ. Uravn., 34:10 (1998), 1299–1303
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Ivan Tarielovich Kiguradze (on the occasion of his sixtieth birthday)
Differ. Uravn., 33:1 (1997), 6–11
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Восьмой Международный конгресс по математическому образованию
Mat. Pros., Ser. 3, 1 (1997), 175–191
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Fourth International Conference “Mathematics. Computer. Education”
Uspekhi Mat. Nauk, 52:6(318) (1997), 209–210
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Otakar Boruvka [1899–1995]
Differ. Uravn., 31:10 (1995), 1770–1771
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Письмо в редакцию
Differ. Uravn., 30:11 (1994), 2020
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Anatolii Sergeevich Kalashnikov (on his sixtieth birthday)
Uspekhi Mat. Nauk, 49:4(298) (1994), 189–190
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Obituary: Teǐmuraz Ambros'evich Chanturiya
Differ. Uravn., 26:12 (1990), 2190–2191
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Inter-College School-Seminar “Differential Equations and Their Applications”
Uspekhi Mat. Nauk, 42:5(257) (1987), 236–238
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Fiftieth anniversary of the Department of Differential Equations at Moscow University
Uspekhi Mat. Nauk, 41:3(249) (1986), 219–223
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Sessions of the Petrovskii Seminar on differential equations and mathematical problems of physics
Uspekhi Mat. Nauk, 39:5(239) (1984), 253–260
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In memory of Boris Pavlovich Demidovich (obituary)
Uspekhi Mat. Nauk, 33:2(200) (1978), 169–174
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All-Union Conference-Seminar of Chairmen of University Mathematics Departments
Uspekhi Mat. Nauk, 31:2(188) (1976), 247–253
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Mathematical manuscripts of Karl Marx
Uspekhi Mat. Nauk, 23:5(143) (1968), 205–211
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International Congress of Mathematicians (Moscow, 1966)
Uspekhi Mat. Nauk, 22:4(136) (1967), 137–143
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