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

2008/04/23 by Pavel V. Kuptsov, Kuptsov, Pavel V., Sergey P. Kuznetsov +3
Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #nlin.CD

paper · pdf · doi:10.48550/arxiv.0804.3677

17 pages, 8 figures

arxiv created 2008/04/23 · arxiv updated 2009/12/01

Abstract

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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