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Kaschenko Sergey Aleksandrovich

Publications in Math-Net.Ru

  1. Local dynamics of aperiodic chains with unidirectional couplings

    Izvestiya VUZ. Applied Nonlinear Dynamics, 34:1 (2026),  9–33
  2. Piecewise constant modes of operation of fully coupled networks and their limit integro-differential systems

    Model. Anal. Inform. Sist., 32:2 (2025),  206–224
  3. Simulation of Delay Using a System of Ordinary Differential Equations

    Mat. Zametki, 118:2 (2025),  240–257
  4. Dynamical Properties of Periodic Solutions of Integro-Differential Equations

    Rus. J. Nonlin. Dyn., 21:1 (2025),  49–67
  5. Local and Nonlocal Cycles in a System with Delayed Feedback Having Compact Support

    Regul. Chaotic Dyn., 30:1 (2025),  103–119
  6. Dynamics of second-order equations with impulse-type delayed feedback

    Uspekhi Mat. Nauk, 80:1(481) (2025),  159–160
  7. Stability of solutions to the logistic equation with delay, diffusion, and nonclassical boundary conditions

    Dokl. RAN. Math. Inf. Proc. Upr., 517 (2024),  101–108
  8. Quasinormal forms for systems of two equations with large delay

    Izvestiya VUZ. Applied Nonlinear Dynamics, 32:6 (2024),  782–795
  9. Chains with Diffusion-Type Couplings Containing a Large Delay

    Mat. Zametki, 115:3 (2024),  355–370
  10. Asymptotics of Self-Oscillations in Chains of Systems of Nonlinear Equations

    Regul. Chaotic Dyn., 29:1 (2024),  218–240
  11. Wave propagation in the Kolmogorov–Petrovsky–Piscounov–Fisher equation with delay

    TMF, 220:3 (2024),  415–435
  12. A family of piecewise-smooth solutions of a class of spatially distributed equations

    CMFD, 69:2 (2023),  263–275
  13. Dynamics of a system of two equations with a large delay

    Dokl. RAN. Math. Inf. Proc. Upr., 513 (2023),  51–56
  14. Dynamics of full-coupled chains of a great number of oscillators with a large delay in couplings

    Izvestiya VUZ. Applied Nonlinear Dynamics, 31:4 (2023),  523–542
  15. Bifurcations in the Logistic Equation with Diffusion and Delay in the Boundary Condition

    Mat. Zametki, 113:6 (2023),  940–944
  16. Local dynamics of the model of a semiconductor laser with delay

    TMF, 215:2 (2023),  232–241
  17. Dynamics of chains of many oscillators with unidirectional and bidirectional delay coupling

    Zh. Vychisl. Mat. Mat. Fiz., 63:10 (2023),  1617–1636
  18. Quasi-normal forms in the problem of vibrations of pedestrian bridges

    Dokl. RAN. Math. Inf. Proc. Upr., 506 (2022),  49–53
  19. Dynamics of the chain of logistic equations with delay and antidiffusive linkage

    Dokl. RAN. Math. Inf. Proc. Upr., 502 (2022),  23–27
  20. The influence of external environment resistance coefficient on population dynamics

    Izv. Vyssh. Uchebn. Zaved. Mat., 2022, no. 1,  65–73
  21. Local dynamics of laser chain model with optoelectronic delayed unidirectional coupling

    Izvestiya VUZ. Applied Nonlinear Dynamics, 30:2 (2022),  189–207
  22. Asymptotics of the Relaxation Cycle in the Modified Logistic Equation with Delay

    Mat. Zametki, 112:1 (2022),  143–147
  23. Construction of families of equations to describe irregular solutions in the Fermi–Pasta–Ulam problem

    Dokl. RAN. Math. Inf. Proc. Upr., 501 (2021),  52–56
  24. Dynamics of Spatially Distributed Chains of Coupled Systems of Equations in a Two-Dimensional Domain

    Mat. Zametki, 110:5 (2021),  715–725
  25. Comparative dynamics of chains of coupled van der Pol equations and coupled systems of van der Pol equations

    TMF, 207:2 (2021),  277–292
  26. Corporate dynamics in chains of coupled logistic equations with delay

    Zh. Vychisl. Mat. Mat. Fiz., 61:7 (2021),  1070–1081
  27. Bifurcations in a delay logistic equation under small perturbations

    Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 10,  47–64
  28. Estimation of the region of global stability of the equilibrium state of the logistic equation with delay

    Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 9,  39–55
  29. Normalized boundary value problems in the model of optoelectronic oscillator delayed

    Izvestiya VUZ. Applied Nonlinear Dynamics, 28:4 (2020),  361–382
  30. Features of the algorithmic implementation of difference analogues of the logistic equation with delay

    Model. Anal. Inform. Sist., 27:3 (2020),  344–355
  31. Family of finite-dimensional maps induced by a logistic equation with a delay

    Mat. Model., 32:3 (2020),  19–46
  32. Local Dynamics of Chains of Van der Pol Coupled Systems

    Mat. Zametki, 108:6 (2020),  936–940
  33. Andronov–Hopf Bifurcation in Logistic Delay Equations with Diffusion and Rapidly Oscillating Coefficients

    Mat. Zametki, 108:1 (2020),  47–63
  34. Dynamics of a System of Two Simple Self-Excited Oscillators with Delayed Step-by-Step Feedback

    Rus. J. Nonlin. Dyn., 16:1 (2020),  23–43
  35. Bifurcations in spatially distributed chains of two-dimensional systems of equations

    Uspekhi Mat. Nauk, 75:6(456) (2020),  171–172
  36. Asymptotic behavior of rapidly oscillating solutions of the modified Camassa–Holm equation

    TMF, 203:1 (2020),  40–55
  37. Asymptotics of regular solutions to the Camassa–Holm problem

    Zh. Vychisl. Mat. Mat. Fiz., 60:2 (2020),  253–266
  38. Equations with the Fermi-Pasta-Ulam and dislocations nonlinearity

    Izvestiya VUZ. Applied Nonlinear Dynamics, 27:4 (2019),  52–70
  39. Dynamics of equation with two delays modelling the number of population

    Izvestiya VUZ. Applied Nonlinear Dynamics, 27:2 (2019),  21–38
  40. Homogenization over the spatial variable in nonlinear parabolic systems

    Tr. Mosk. Mat. Obs., 80:1 (2019),  63–86
  41. Bifurcations Due to the Variation of Boundary Conditions in the Logistic Equation with Delay and Diffusion

    Mat. Zametki, 106:1 (2019),  138–143
  42. Asymptotics of rapidly oscillating solutions of the generalized Korteweg–de Vries–Burgers equation

    Uspekhi Mat. Nauk, 74:4(448) (2019),  181–182
  43. Analysis of local dynamics of difference and close to them differential-difference equations

    Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 9,  29–41
  44. Bifurcations in the generalized Korteweg–de Vries equation

    Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 2,  54–68
  45. Dynamics of two-component parabolic systems of Schrödinger type

    Izvestiya VUZ. Applied Nonlinear Dynamics, 26:5 (2018),  81–100
  46. Features of the local dynamics of the opto-electronic oscillator model with delay

    Model. Anal. Inform. Sist., 25:1 (2018),  71–82
  47. The simplest critical cases in the dynamics of nonlinear systems with small diffusion

    Tr. Mosk. Mat. Obs., 79:1 (2018),  97–115
  48. Application of the Averaging Principle to the Study of the Dynamics of the Delay Logistic Equation

    Mat. Zametki, 104:2 (2018),  216–230
  49. Regular and irregular solutions in the problem of dislocations in solids

    TMF, 195:3 (2018),  362–380
  50. Dynamics of a delay logistic equation with slowly varying coefficients

    Zh. Vychisl. Mat. Mat. Fiz., 58:12 (2018),  1999–2013
  51. Stability of the solutions of the simplest space-distributed discrete equations

    Model. Anal. Inform. Sist., 24:5 (2017),  537–549
  52. About bifurcations at small perturbations in a logistic equation with delay

    Model. Anal. Inform. Sist., 24:2 (2017),  168–185
  53. Asymptotic of eigenvalues of periodic and antiperiodic boundary value problem for second order differential equations

    Model. Anal. Inform. Sist., 24:1 (2017),  13–30
  54. Periodic Solutions of Nonlinear Equations Generalizing Logistic Equations with Delay

    Mat. Zametki, 102:2 (2017),  216–230
  55. Bifurcations in Kuramoto–Sivashinsky equations

    TMF, 192:1 (2017),  23–40
  56. Rapidly oscillating solutions of a generalized Korteweg–de Vries equation

    Zh. Vychisl. Mat. Mat. Fiz., 57:11 (2017),  1812–1823
  57. Two wave interactions in a Fermi–Pasta–Ulam model

    Model. Anal. Inform. Sist., 23:5 (2016),  548–558
  58. Asymptotic expansions of eigenvalues of periodic and antiperiodic boundary problems for singularly perturbed second order differential equation with turning points

    Model. Anal. Inform. Sist., 23:1 (2016),  61–85
  59. Asymptotic expansions of eigenvalues of the first boundary problem for singularly perturbed second order differential equation with turning points

    Model. Anal. Inform. Sist., 23:1 (2016),  41–60
  60. Local dynamics of two-component singularly perturbed parabolic systems

    Tr. Mosk. Mat. Obs., 77:1 (2016),  67–82
  61. The Dynamics of Second-order Equations with Delayed Feedback and a Large Coefficient of Delayed Control

    Regul. Chaotic Dyn., 21:7-8 (2016),  811–820
  62. Asymptotics of eigenvalues of first boundary value problem for singularly pertubed second-order differential equation with turning points

    Model. Anal. Inform. Sist., 22:5 (2015),  682–710
  63. Dynamical properties of the Fisher–Kolmogorov–Petrovskii–Piscounov equation with deviation of the spatial variable

    Model. Anal. Inform. Sist., 22:5 (2015),  609–628
  64. Corporate dynamics of systems of logistic delay equations with large delay control

    Model. Anal. Inform. Sist., 22:3 (2015),  372–391
  65. Fisher–Kolmogorov–Petrovskii–Piscounov equation with delay

    Model. Anal. Inform. Sist., 22:2 (2015),  304–321
  66. Dynamics of the Logistic Equation with Delay

    Mat. Zametki, 98:1 (2015),  85–100
  67. Dynamics of strongly coupled spatially distributed logistic equations with delay

    Zh. Vychisl. Mat. Mat. Fiz., 55:4 (2015),  610–620
  68. Local dynamics of difference and difference-differential equations

    Izvestiya VUZ. Applied Nonlinear Dynamics, 22:1 (2014),  71–92
  69. The dynamics of the logistic equation with delay and delayed control

    Model. Anal. Inform. Sist., 21:5 (2014),  61–77
  70. Asymptotics of a Steady-State Condition of Finite-Difference Approximation of a Logistic Equation with Delay and Small Diffusion

    Model. Anal. Inform. Sist., 21:1 (2014),  94–114
  71. Local Dynamics of a Logistic Equation with Delay

    Model. Anal. Inform. Sist., 21:1 (2014),  73–88
  72. Local dynamics of an equation with large delay and distributed deviation of the space variable

    Sibirsk. Mat. Zh., 55:2 (2014),  315–323
  73. Spatially distributed control of the dynamics of the logistic delay equation

    Zh. Vychisl. Mat. Mat. Fiz., 54:6 (2014),  953–968
  74. Dynamics of the logistic delay equation with a large spatially distributed control coefficient

    Zh. Vychisl. Mat. Mat. Fiz., 54:5 (2014),  766–778
  75. Local Dynamics of a Laser with Rapidly Oscillating Parameters

    Model. Anal. Inform. Sist., 20:5 (2013),  45–61
  76. Relaxation Oscillations in Models of Multi-Species Biocenose

    Model. Anal. Inform. Sist., 20:5 (2013),  5–24
  77. Parametric Resonance in the Logistic Equation with Delay under a Two-Frequency Perturbation

    Model. Anal. Inform. Sist., 20:3 (2013),  86–98
  78. Relaxation Oscillations in a System with Delays Modeling the Predator–Prey Problem

    Model. Anal. Inform. Sist., 20:1 (2013),  52–98
  79. Quasinormal Forms for Lang–Kobayashi Equations with a Large Control Coefficient

    Model. Anal. Inform. Sist., 20:1 (2013),  18–29
  80. Dynamics of a Complex Spatially Distributed Hutchinson Equation

    Model. Anal. Inform. Sist., 19:5 (2012),  35–39
  81. Stationary States of a Delay Differentional Equation of Insect Population's Dynamics

    Model. Anal. Inform. Sist., 19:5 (2012),  18–34
  82. Asymptotics of Solutions of the Generalized Hutchinson's Equation

    Model. Anal. Inform. Sist., 19:3 (2012),  32–61
  83. The dynamics of Kuramoto equation with spatially-distributed control

    Model. Anal. Inform. Sist., 19:1 (2012),  24–35
  84. The asymptotic of periodic solutions of autonomous parabolic equations with rapidly oscillating coefficients and equations with large diffusion coefficients

    Model. Anal. Inform. Sist., 19:1 (2012),  7–23
  85. Quasi-normal forms for parabolic systems with strong nonlinearity and weak diffusion

    Zh. Vychisl. Mat. Mat. Fiz., 52:8 (2012),  1482–1491
  86. Principal quasinormal forms for two-component systems of parabolic equations

    Model. Anal. Inform. Sist., 18:3 (2011),  12–20
  87. Spatially inhomogeneous periodic solutions in the Hutchinson equation with distributed saturation

    Model. Anal. Inform. Sist., 18:1 (2011),  37–45
  88. Dynamics of a quasi-linear boundary problem generalizing the equation with large delay

    Model. Anal. Inform. Sist., 18:1 (2011),  28–31
  89. Local dynamics of DDE with large delay in the vicinity of the self-similar cycle

    Model. Anal. Inform. Sist., 17:3 (2010),  38–47
  90. Multistability in a laser model with large delay

    Model. Anal. Inform. Sist., 17:2 (2010),  17–27
  91. Spatially inhomogeneous periodic solutions in distributed Hutchinson equation

    Model. Anal. Inform. Sist., 16:4 (2009),  77–85
  92. Complex oscillation in systems of two and three spiking neurons

    Model. Anal. Inform. Sist., 15:2 (2008),  72–74
  93. Relaxation oscillations in the simplest models with delay

    Model. Anal. Inform. Sist., 15:2 (2008),  55–60
  94. New researches in systems analysis and computation modeling of Russian educational strategy and politics

    Keldysh Institute preprints, 2001, 089
  95. Bifurcations in the neighborhood of a cycle under small perturbations with a large delay

    Zh. Vychisl. Mat. Mat. Fiz., 40:5 (2000),  693–702
  96. Local dynamics of nonlinear singularly perturbed systems with delay

    Differ. Uravn., 35:10 (1999),  1343–1355
  97. Dynamics of equations with feedback of impulse type

    Differ. Uravn., 35:7 (1999),  889–898
  98. Asymptotic analysis of the auto-generators dynamics with different non-linear delay feedback

    Fundam. Prikl. Mat., 5:4 (1999),  1027–1060
  99. Bifurcation peculiarities of a singularly perturbed equation with delay

    Sibirsk. Mat. Zh., 40:3 (1999),  567–572
  100. The Ginzburg–Landau equation as a normal form for a second-order difference-differential equation with a large delay

    Zh. Vychisl. Mat. Mat. Fiz., 38:3 (1998),  457–465
  101. Wave structures in ring neuron systems

    Mat. Model., 9:3 (1997),  29–39
  102. Oscillations in systems of equations with delay and difference diffusion that model local neural networks

    Dokl. Akad. Nauk, 344:3 (1995),  319–322
  103. Wave structures in ring systems of homogeneous neuron modules

    Dokl. Akad. Nauk, 342:3 (1995),  318–321
  104. Asymptotics of relaxation oscillations in systems of differential-difference equations with a compactly supported nonlinearity. II

    Differ. Uravn., 31:12 (1995),  1968–1976
  105. Asymptotics of relaxation oscillations in systems of differential-difference equations with a compactly supported nonlinearity. I

    Differ. Uravn., 31:8 (1995),  1330–1339
  106. Poincaré mappings in laser models with periodic modulation of the parameters

    Differ. Uravn., 31:1 (1995),  16–22
  107. Wave distribution in simplest ring neural structures

    Mat. Model., 7:12 (1995),  3–18
  108. The construction of normalized systems for investigating the dynamics of hybrid and hyperbolic equations

    Zh. Vychisl. Mat. Mat. Fiz., 34:4 (1994),  564–575
  109. Investigation of oscillations in ring neural structures

    Dokl. Akad. Nauk, 333:5 (1993),  594–597
  110. Asymptotics of nonregular oscillations in a model of a self-induced generator with delayed feedback

    Dokl. Akad. Nauk, 328:2 (1993),  174–177
  111. On a differential-difference equation modeling neuron impulse activity

    Mat. Model., 5:12 (1993),  13–25
  112. Rapidly oscillating traveling waves in systems with small diffusion

    Differ. Uravn., 28:2 (1992),  254–262
  113. Asymptotic investigation of multistability phenomena in laser models with opto-electronic feedback

    Dokl. Akad. Nauk SSSR, 316:2 (1991),  327–331
  114. Relaxation oscillations in a system of equations describing the operation of a solid-state laser with a nonlinear element of delaying action

    Differ. Uravn., 27:5 (1991),  752–758
  115. Asymptotic form of spatially non-uniform structures in coherent nonlinear optical systems

    Zh. Vychisl. Mat. Mat. Fiz., 31:3 (1991),  467–473
  116. The local dynamics of two-component contrast structures in the neighborhood of a bifurcation point

    Dokl. Akad. Nauk SSSR, 312:2 (1990),  345–350
  117. Spatial heterogeneous structures in the simplest models with delay and diffusion

    Mat. Model., 2:9 (1990),  49–69
  118. Application of asymptotic methods for investigation of stationary regimes of generation in lasers with delay element

    Mat. Model., 2:4 (1990),  97–120
  119. Multistability and chaos in a negative-feedback laser

    Kvantovaya Elektronika, 17:8 (1990),  1023–1028
  120. Asymptotic behaviour of rapidly oscillating contrasting spatial structures

    Zh. Vychisl. Mat. Mat. Fiz., 30:2 (1990),  254–269
  121. Short-wave bifurcations in systems with small diffusion

    Dokl. Akad. Nauk SSSR, 307:2 (1989),  269–273
  122. Complex periodic solutions of a system of differential-difference equations with small diffusion

    Dokl. Akad. Nauk SSSR, 306:1 (1989),  35–38
  123. Application of the normalization method to the study of the dynamics of a differential-difference equation with a small factor multiplying the derivative

    Differ. Uravn., 25:8 (1989),  1448–1451
  124. Spatial singularities of high-mode bifurcations of two-component systems with small diffusion

    Differ. Uravn., 25:2 (1989),  262–270
  125. Quasinormal forms for parabolic equations with small diffusion

    Dokl. Akad. Nauk SSSR, 299:5 (1988),  1049–1052
  126. On miniversal deformations of matrices

    Uspekhi Mat. Nauk, 43:1(259) (1988),  201–202
  127. Steady regimes of the Hutchinson equation with diffusion

    Dokl. Akad. Nauk SSSR, 292:2 (1987),  327–330
  128. Investigation of the asymptotic behavior of periodic solutions of autonomous parabolic equations by methods of the larger parameter

    Differ. Uravn., 23:2 (1987),  283–292
  129. Bifurcation of self-oscillations of nonlinear parabolic equations with small diffusion

    Mat. Sb. (N.S.), 130(172):4(8) (1986),  488–499
  130. Asymptotics of periodic solutions of autonomous parabolic equations with small diffusion

    Sibirsk. Mat. Zh., 27:6 (1986),  116–127
  131. Diffusion instability of a torus

    Dokl. Akad. Nauk SSSR, 281:6 (1985),  1307–1309
  132. Optimization of the hunting process

    Differ. Uravn., 21:10 (1985),  1706–1709
  133. Stationary modes of an equation describing fluctuations of an insect population

    Dokl. Akad. Nauk SSSR, 273:2 (1983),  328–330
  134. Investigation, by large parameter methods, of a system of nonlinear differential-difference equations modeling a predator-prey problem

    Dokl. Akad. Nauk SSSR, 266:4 (1982),  792–795
  135. Parametric resonance in systems with lag under two-frequency perturbation

    Sibirsk. Mat. Zh., 21:2 (1980),  113–118
  136. A test for the stability of the solutions of singularly perturbed second order equations with periodic coefficients

    Uspekhi Mat. Nauk, 29:4(178) (1974),  171–172

  137. Leonid Pavlovich Shil'nikov (obituary)

    Uspekhi Mat. Nauk, 67:3(405) (2012),  175–178
  138. Dynamics of spikes in delay coupled semiconductor lasers

    Regul. Chaotic Dyn., 15:2-3 (2010),  319–327

© Steklov Math. Inst. of RAS, 2026