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

For citation:

Arzhanukhina D. S. On scenarios of hyperbolic chaos destruction in model maps on torus with dissipative perturbation. Izvestiya VUZ. Applied Nonlinear Dynamics, 2012, vol. 20, iss. 1, pp. 117-123. DOI: 10.18500/0869-6632-2012-20-1-117-123

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 2012no1p117.pdf
(downloads: 139)
Language: 
Russian
Heading: 
Bifurcations in Dynamical Systems
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/0869-6632-2012-20-1-117-123

On scenarios of hyperbolic chaos destruction in model maps on torus with dissipative perturbation

Autors: 
Arzhanukhina Darja Sergeevna, Saratov State University
Abstract: 

In this paper we investigate modified «Arnold cat» map with dissipative terms, in which a hyperbolic chaos exists for small perturbation magnitudes, and in a certain range a hyperbolic chaotic attractor with Cantor transversal structure takes place, collapsing with a further perturbation amplitude increase.

Key words: 
Attractor
hyperbolic chaos
Lyapunov exponent
Reference: 
  1. Kuznetsov SP. Dynamical Chaos: Course of Lectures. Moscow: Fizmatlit; 2001. 296 p. (in Russian).
  2. Berger P, Pomo I, Vidal K. Order in chaos. About the deterministic approach to turbulence. Moscow: Mir; 1991. 368 p. (in Russian).
  3. Schuster G. Deterministic Chaos. An Introduction. Moscow: Mir; 1988. 240 p. (in Russian).
  4. Lichtenberg AJ, Lieberman MA. Regular and Stochastic Motion. New York: Springer-Verlag; 1983. 499 p.
  5. Anishchenko VS, Vadivasova TE, Astakhov VV. Nonlinear dynamics of chaotic and stochastic systems. Fundamental principles and selected issues. Saratov: Saratov Univ. Publ.; 1999. 368 p.
  6. Kuznetsov SP. Hyperbolic strange attractors of physically realizable systems. Izvestiya VUZ. Applied Nonlinear Dynamics. 2009;17(4):5–34 (in Russian). DOI: 10.18500/0869-6632-2009-17-4-5-34.
  7. Kuznetsov SP. An example of a non-autonomous continuous-time system with attractor of Plykin type in the Poincare map. Nelin. Dinam. 2009;5(3):403–424 (in Russian).
  8. Kuznetsov SP. Dynamical chaos and uniformly hyperbolic attractors: from mathematics to physics. Phys. Usp. 2011;54(2):119–144. DOI: 10.3367/UFNe.0181.201102a.0121.
  9. Kuznetsov SP, Seleznev EP. A strange attractor of the Smale-Williams type in the chaotic dynamics of a physical system. Journal of Experimental and Theoretical Physics. 2006;102(2):355–364. DOI: 10.1134/S1063776106020166.
  10. Belykh V, Belykh I, Mosekilde E. Hyperbolic Plykin attractor can exist in neuron models. International Journal of Bifurcation and Chaos. 2005;15(11):3567–3578. DOI: 10.1142/S0218127405014222.
  11. Katok A, Hasselblatt B. Introduction to the Modern Theory of Dynamical Systems. Cambridge: Cambridge University Press; 1999. 768 p.
Received: 
13.02.2012
Accepted: 
13.02.2012
Published: 
20.04.2012
Short text (in English):
PDF icon a2012no1p117.pdf
(downloads: 97)
  • 1724 reads