Analysis of Two Time Scale Property of Singularly Perturbed System on Chaotic Attractor

TL;DR

This paper explores the two time scale property of singularly perturbed systems on chaotic attractors, proposing that the orderly structure of chaotic attractors can aid in analyzing multi-scale behaviors.

Contribution

It introduces a novel approach to analyze two time scale properties of singularly perturbed systems within chaotic attractors, highlighting the utility of chaotic attractor orderliness.

Findings

Chaotic attractors exhibit orderly structures useful for analysis.

Two time scale behavior can be characterized on chaotic attractors.

The approach provides new insights into nonlinear system analysis.

Abstract

The idea that chaos could be a useful tool for analyze nonlinear systems considered in this paper and for the first time the two time scale property of singularly perturbed systems is analyzed on chaotic attractor. The general idea introduced here is that the chaotic systems have orderly strange attractors in phase space and this orderly of the chaotic systems in subscription with other classes of systems can be used in analyses. Here the singularly perturbed systems are subscripted with chaotic systems. Two time scale property of system is addressed. Orderly of the chaotic attractor is used to analyze two time scale behavior in phase plane.