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Recently, a system with uniformly hyperbolic attractor of Smale-Williams typehas been suggested [Kuznetsov, Phys. Rev. Lett., 95, 144101, 2005]. This systemconsists of two coupled non-autonomous van der Pol oscillators and admitssimple physical realization. In present paper we introduce amplitude equationsfor this system and prove that the attractor of the system of amplitudeequations is also uniformly hyperbolic. Also we represent qualitativeillustrations as well as quantitative characteristics of a chaotic dynamics onthis attractor.

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