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

For citation:

Pozdnyakov M. V., Savin A. V. Multistable regimes in asymmetrically coupled period-­doubling systems. Izvestiya VUZ. Applied Nonlinear Dynamics, 2010, vol. 18, iss. 5, pp. 44-53. DOI: 10.18500/0869-6632-2010-18-5-44-53

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
PDF icon 2010no5p045.pdf
(downloads: 157)
Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/0869-6632-2010-18-5-44-53

Multistable regimes in asymmetrically coupled period-­doubling systems

Autors: 
Pozdnyakov Mihail Valerevich, Saratov State University
Savin Aleksej Vladimirovich, Saratov State University
Abstract: 

Multistable regimes in asymmetrically coupled logistic maps are investigated. The evolution of the multistability regions in the parameter plane and the basins of coexisting attractors are revealed.

Key words: 
multistability
period-doublings
Reference: 
  1. Anishchenko VS, Vadivasova TE, Astakhov VV. Nonlinear dynamics of chaotic and stochastic systems. Saratov: Saratov Univ. Publ.; 1999. 368 p. (in Russian).
  2. Astakhov VV, Bezruchko BP, Erastova EN, Seleznev YP. Types of oscillations and their evolution in dissipatively-related Feigenbaum systems. Tech. Phys. 1990;60(10):19–26 (in Russian).
  3. Astakhov VV, Bezruchko BP, Gulyaev YV, Seleznev EP. Multistable states of dissipatively-connected Feigenbaum systems. Tech. Phys. Lett. 1988;15(3):60–65 (in Russian).
  4. 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.
  5. Feudel U. Complex dynamics in multistable systems. International Journal of Bifurcation and Chaos. 2008;18(6):1607–1626. DOI: 10.1142/S0218127408021233.
  6. Fujisaka H, Yamada Y. Stability theory of synchronized motions in coupled oscillatory systems. Progr. Theor. Phys. 1983;69:32–47. DOI: 10.1143/PTP.69.32.
  7. Postnov DE, Vadivasova ТЕ, Sosnovstseva OV, Balanov AG, Mosekilde E. Role of multistability in the transition to chaotic phase synchronization. Chaos. 1999;9:227–232. DOI: 10.1063/1.166394.
  8. Vadivasova TE, Sosnovtseva OV, Balanov AG, Astakhov VV. Phase multistability of synchronous chaotic oscillations. Discrete dynamics in Society and Nature. 2000;4:231–243. DOI: 10.1155/S1026022600000224.
  9. Sosnovtseva OV, Postnov DE, Nekrasov AM, Mosekilde E, Holstein-Rathlou NH. Phase multistability of self-modulated oscillators. Phys. Rev. E. 2002;66:0362. DOI: 10.1103/PhysRevE.66.036224.
  10. 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.
  11. Kuznetsov SP. Critical behavior of one-dimensional chains. Sov. Tech. Phys. Lett. 1983;9:94–98 (in Russian).
  12. Kuznetsov SP. Dynamic Chaos. Moscow: Fizmatlit; 2006. 356 p. (in Russian).
  13. Feudel U, Grebogi C, Hunt BR, Yorke JA. Map with more than 100 coexisting low-period periodic attractors. Phys. Rev. E. 1996;54(1):71–81. DOI: 10.1103/physreve.54.71.
  14. Kuznetsov AP, Savin AV, Savin DV. Features in dynamics of an almost conservative Ikeda map. Technical Physics Letters. 2007;33(2):122–124. DOI: 10.1134/S1063785007020095.
Received: 
03.12.2009
Accepted: 
20.05.2010
Published: 
31.12.2010
Short text (in English):
PDF icon a2010no5p045.pdf
(downloads: 99)
  • 1932 reads