Numerical test for hyperbolicity in chaotic systems with multiple time delays

TL;DR

This paper extends a method for verifying hyperbolicity in chaotic systems with multiple time delays, enabling efficient analysis of high-dimensional delay systems using covariant Lyapunov vectors.

Contribution

It introduces an extended fast angles method for hyperbolicity testing applicable to complex delay systems with high-dimensional phase spaces.

Findings

Hyperbolicity confirmed in analyzed delay systems

Method effective for high-dimensional systems

Applicable to systems with arbitrary delay loops

Abstract

We develop an extension of the fast method of angles for hyperbolicity verification in chaotic systems with an arbitrary number of time-delay feedback loops. The adopted method is based on the theory of covariant Lyapunov vectors and provides an efficient algorithm applicable for systems with high-dimensional phase space. Three particular examples of time-delay systems are analyzed and in all cases the expected hyperbolicity is confirmed.