VERIFICATION OF HYPERBOLICITY CONDITIONS FOR A CHAOTIC ATTRACTOR IN A SYSTEM OF COUPLED NONAUTONOMOUS VAN DER POL OSCILLATORS

Izvestiya Vysshikh Uchebnykh Zavedeniy. Prikladnaya Nelineynaya Dinamika

Volumn 14, Issue 5, 2006, Pages 3-29

  Kuznetsov, S P ^a   Sataev, I R ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77951163799     PISSN: 08696632     EISSN: 25421905     Source Type: Journal    
DOI: 10.18500/0869-6632-2006-14-5-3-29     Document Type: Article

References (12)

1. Devaney R.L. An Introduction to Chaotic Dynamical Systems. NY: Addison-Wesley, 1989.
2. Shilnikov L. Mathematical problems of nonlinear dynamics: A Tutorial // Int. J. of Bifurcation and Chaos. 1997. Vol. 7, N 9. P. 1353.
3. Afraimovich V. and Hsu S.-B. Lectures on chaotic dynamical systems // AMS/IP Studies in Advanced Mathematics, Vol. 28, American Mathematical Society, Providence, RI; International Press, Somerville, MA, 2003.
4. Ott E. Chaos in Dynamical Systems. Cambridge University Press, 1993.
5. Hunt T.J. and MacKay R.S. Anosov parameter values for the triple linkage and a physical system with a uniformly chaotic attractor// Nonlinearity. 2003. Vol. 16. P. 499.
6. Hunt T.J. Low Dimensional Dynamics: Bifurcations of Cantori and Realisations of Uniform Hyperbolicity. PhD Thesis, Univ. of Cambridge, 2000 (http://www.timhunt.me.uk/maths/thesis.ps.gz).
7. Belykh V., Belykh I. and Mosekilde The hyperbolic Plykin attractor can exist in neuron models// Int. J. of Bifurcation and Chaos. 2005. Vol. 15, N 11. P. 3567.
8. Kuznetsov S.P. Example of a physical system with a hyperbolic attractor of the Smale-Williams type// Phys. Rev. Lett. 2005. Vol. 95. P. 44101.
9. LAPACK - Linear Algebra PACKage, version 3.0. May, 2000 (http://www.netlib.org/lapack).
10. Benettin G., GalganiL., GiorgilliA., Strelcyn J.-M. Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems: A method for computing all of them. Part {I}: Theory. Part {II}: Numerical application// Meccanica. 1980. Vol. 15. P. 9.
11. Bunimovich L.A., Sinai Ya.G. Statistical mechanics of coupled map lattices// Theory and application of coupled map lattices/Ed. by K.Kaneko. John Wiley & Sons Ltd, 1993. P. 169.
12. Bunimovich L.A., Sinai Ya.G. Spacetime chaos in coupled map lattices// Nonlinearity. 1988. Vol. 1. P. 491.