Autonomous coupled oscillators with hyperbolic strange attractors

Physica D: Nonlinear Phenomena

Volumn 232, Issue 2, 2007, Pages 87-102

  Kuznetsov, Sergey P ^a   Pikovsky, Arkady ^b  

^a INSTITUTE OF RADIO ENGINEERING AND ELECTRONICS   (Russian Federation)

^b UNIVERSITY OF POTSDAM   (Germany)

Author keywords

Arnold cat map; Coupled oscillators; Hyperbolic systems; Smale Williams strange attractor

Indexed keywords

CHAOTIC SYSTEMS; CONTROL NONLINEARITIES; LYAPUNOV FUNCTIONS; MATHEMATICAL MODELS; TWO DIMENSIONAL;

ARNOLD CAT MAPS; COUPLED OSCILLATORS; HYPERBOLIC SYSTEMS; SMALE-WILLIAMS STRANGE ATTRACTORS;

OSCILLATORS (ELECTRONIC);

EID: 34547138184     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2007.05.008     Document Type: Article

References (16)

1. Katok A., and Hasselblatt B. Introduction to the Modern Theory of Dynamical Systems (1995), Cambridge University Press
2. Plykin R. Sources and sinks for A-diffeomorphismes of surfaces. Math. USSR, Sb. 23 (1974) 233-253
3. m, m ≥ 3. Comm. Math. Phys. 64 (1978) 35-40
4. T. Hunt, Low dimensional dynamics: Bifurcations of Cantori and realisations of uniform hyperbolicity. Ph.D. Thesis, University of Cambridge, 2000
5. Belykh V.N., Belykh I.V., and Mosekilde E. Hyperbolic Plykin attractor can exist in neuron models. Int. J. Bifurc. Chaos 15 (2005) 3567-3578
6. Shilnikov L.P., and Turaev D.V. Simple bifurcations leading to hyperbolic attractors. Comput. Math. Appl. 34 2-4 (1997) 173-193
7. Shilnikov L.P. Mathematical problems of nonlinear dynamics: A tutorial. Int. J. Bifurc. Chaos 7 (1997) 1353-2001
8. Kuznetsov S.P. Example of a physical system with a hyperbolic attractor of the Smale-Williams type. Phys. Rev. Lett. 95 (2005) 144101
9. Kuznetsov S.P., and Seleznev E.P. A strange attractor of the Smale-Williams type in the chaotic dynamics of a physical system. J. Exp. Theor. Phys. 102 2 (2006) 355-364
10. Isaeva O.B., Jalnine A.Yu., and Kuznetsov S.P. Arnold's cat map dynamics in a system of coupled non-autonomous van der Pol oscillators. Phys. Rev. E 74 (2006) 046207
11. Jalnine A.Yu., and Kuznetsov S.P. On a possibility of realization of a strange nonchaotic attractor of Hunt and Ott in a physical system. Tech. Phys. 52 (2007) 401-408
12. P. Gaspard, Maps. Encyclopedia of Nonlinear Science, Routledge, New York, 548-553, 2005
13. Guckenheimer J., and Holmes P. Structurally stable heteroclinic cycles. Math. Proc. Cambridge Philos. Soc. 103 (1988) 189-192
14. Ott E. Chaos in Dynamical Systems (1992), Cambridge Univ. Press, Cambridge
15. Pazó D., and Mathías M.A. Direct transition to high-dimensional chaos through a global bifurcation. Europhys. Lett. 72 2 (2005) 176-182
16. Kuznetsov S.P., and Sataev I.R. Hyperbolic attractor in a system of coupled non-autonomous van der Pol oscillators: Numerical test for expanding and contracting cones. Phys. Lett. A 365 (2007) 97-104