Uniformly hyperbolic attractor of the Smale-Williams type for a Poincar\'e map in the Kuznetsov system

TL;DR

This paper introduces a computer-assisted method to verify uniform hyperbolicity in dynamical systems, successfully applied to a Poincaré map of coupled oscillators exhibiting a Smale-Williams type attractor.

Contribution

It presents a novel algorithm for computer verification of hyperbolicity, demonstrated on a Kuznetsov system with a complex attractor.

Findings

Successfully verified uniform hyperbolicity of the attractor

Applied method to a Poincaré map of coupled oscillators

Confirmed the attractor is of Smale-Williams type

Abstract

We propose a general algorithm for computer assisted verification of uniform hyperbolicity for maps which exhibit a robust attractor. The method has been successfully applied to a Poincare map for a system of coupled non-autonomous van der Pol oscillators. The model equation has been proposed by Kuznetsov and the attractor seems to be of the Smale-Williams type.