ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Pozdnyakov M. V. Dynamic regimes and multistability in the system of non-symmetrically coupled two-dimensional maps with period-doubling and Neimark–Sacker bifurcations. Izvestiya VUZ. Applied Nonlinear Dynamics, 2011, vol. 19, iss. 4, pp. 68-76. DOI: 10.18500/0869-6632-2011-19-4-68-76

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Dynamic regimes and multistability in the system of non-symmetrically coupled two-dimensional maps with period-doubling and Neimark–Sacker bifurcations

Pozdnyakov Mihail Valerevich, Saratov State University

The phenomenon of multistability in the system of coupled universal two-dimensional maps which shows period-doubling and Neimark–Sacker bifurcations is investigated. The decreasing of possible coexisting attractors number, the evolution of the attractor basins, the disappearance of hyperchaos and three-dimensional torus while putting coupling asymmetry are exposed.

  1. Feudel U. Complex dynamics in multistable systems. International Journal of Bifurcation and Chaos. 2008;18(6):1607–1626. DOI: 10.1142/S0218127408021233.
  2. Astakhov VV, Bezruchko BP, Erastova EN, Seleznev EP. Oscillation modes and their evolution in dissipatively coupled Feigenbaum systems. Tech. Phys. 1990;60(10):19–26 (in Russian).
  3. Astakhov VV, Bezruchko BP, Gulyaev YV, Seleznev EP. Multistable states of dissipatively coupled Feigenbaum systems. Tech. Phys. Lett. 1988;15(3):60–65 (in Russian).
  4. Anishchenko VS, Vadivasova TE, Astakhov VV. Nonlinear Dynamics of Chaotic and Stochastic Systems. Saratov: Saratov University Publishing; 1999. 367 p. (in Russian).
  5. Postnov DE, Nekrasov AM. Mechanisms of phase multistability development in interacting 3D-oscillators. Izvestiya VUZ. Applied Nonlinear Dynamics. 2005;13(1):47–62 (in Russian). DOI: 10.18500/0869-6632-2005-13-1-47-62.
  6. Bezruchko BP, Seleznev EP. Basins of attraction for chaotic attractors in coupled systems with period doubling. Tech. Phys. Lett. 1997;23(2):144–146. DOI: 10.1134/1.1261565.
  7. Fujisaka H, Yamada Y. Stability theory of synchronized motions in coupled oscillatory systems. Progr. Theor. Phys. 1983;69(1):32–47. DOI: 10.1143/PTP.69.32.
  8. Postnov DE, Vadivasova TE, Sosnovstseva OV, Balanov AG, and Mosekilde E. Role of multistability in the transition to chaotic phase synchronization. Chaos. 1999;9(1):227–232. DOI: 10.1063/1.166394.
  9. Vadivasova TE, Sosnovtseva OV, Balanov AG, and Astakhov VV. Phase multistability of synchronous chaotic oscillations. Discrete Dynamics in Society and Nature. 2000;4(3):190125. DOI: 10.1155/S1026022600000224.
  10. Sosnovtseva OV, Postnov DE, Nekrasov AM, Mosekilde E, Holstein-Rathlou NH. Phase multistability of self-modulated oscillators. Phys. Rev. E. 2002;66(3):036224. DOI: 10.1103/PhysRevE.66.036224.
  11. Pozdnjakov MV, Savin AV. Multistable regimes in asymmetrically coupled period-­doubling systems. Izvestiya VUZ. Applied Nonlinear Dynamics. 2010;18(5):44–53 (in Russian). DOI: 10.18500/0869-6632-2010-18-5-44-53.
  12. Kuznetsov SP. Dynamic Chaos. Moscow: Fizmatlit; 2006. 356 p. (in Russian).
  13. Kuznetsov SP. On the critical behavior of one-dimensional chains. Tech. Phys. Lett. 1983;9(2):94 (in Russian).
  14. Kuznetsov AP, Kuznetsova AY, Sataev IR. On the critical behavior of a mapping with a Neimark – Sacker bifurcation upon destruction of phase synchronization at the limiting point of the Feigenbaum cascade. Izvestiya VUZ. Applied Nonlinear Dynamics. 2003;11(1):12–18 (in Russian).
  15. Kuznetsov AP, Savin AV, Tyuryukina LV. Introduction to the Physics of Nonlinear Mappings. Saratov: «Nauchnaya Kniga»; 2010. 134 p. (in Russian).  
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