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

TL;DR

This paper introduces amplitude equations for a coupled oscillator system and proves the resulting attractor is uniformly hyperbolic, providing both qualitative and quantitative insights into its chaotic dynamics.

Contribution

It establishes the hyperbolic nature of the attractor in amplitude equations derived from a physical oscillator system, extending previous findings.

Findings

The attractor is proven to be uniformly hyperbolic.

Qualitative and quantitative descriptions of chaotic dynamics are provided.

The system admits a simple physical realization.

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.