Hyperbolic attractor of Smale-Williams type in a system of two coupled non-autonomous amplitude equations

Details Hyperbolic attractor of Smale-Williams type in a system of two coupled non-autonomous amplitude equations Hyperbolic attractor of Smale-Williams type in a system of two coupled non-autonomous amplitude equations

2008-04-23

arxiv.org/abs/0804.3677v1

Nonlinear Sciences

Chaotic Dynamics

17 pages, 8 figures

Scientific paper

Recently, a system with uniformly hyperbolic attractor of Smale-Williams type has been suggested [Kuznetsov, Phys. Rev. Lett., 95, 144101, 2005]. This system consists of two coupled non-autonomous van der Pol oscillators and admits simple physical realization. In present paper we introduce amplitude equations for this system and prove that the attractor of the system of amplitude equations is also uniformly hyperbolic. Also we represent qualitative illustrations as well as quantitative characteristics of a chaotic dynamics on this attractor.

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