Numerical test for hyperbolicity of chaotic dynamics in time-delay systems

TL;DR

This paper introduces a numerical method to assess hyperbolicity in chaotic time-delay systems using angle distributions, confirming hyperbolicity in some cases and identifying nonhyperbolic chaos in others.

Contribution

The authors develop a novel numerical test based on the angle criterion to evaluate hyperbolicity in time-delay chaotic systems.

Findings

Confirmed hyperbolicity in two tested systems.

Identified nonhyperbolic chaos in one system.

Validated the effectiveness of the angle criterion method.

Abstract

We develop a numerical test of hyperbolicity of chaotic dynamics in time-delay systems. The test is based on the angle criterion and includes computation of angle distributions between expanding, contracting and neutral manifolds of trajectories on the attractor. Three examples are tested. For two of them previously predicted hyperbolicity is confirmed. The third one provides an example of a time-delay system with nonhyperbolic chaos.