Complex dynamics, hidden attractors and continuous approximation of a fractional-order hyperchaotic PWC system

TL;DR

This paper introduces a continuous approximation method for fractional-order PWC systems, analyzes a hyperchaotic example revealing hidden attractors without equilibria, and utilizes set-valued analysis and differential inclusions.

Contribution

It presents a novel continuous approximation approach for fractional PWC systems and demonstrates the existence of hidden attractors in a hyperchaotic system without equilibria.

Findings

The system has hidden attractors despite lacking equilibria.

The continuous approximation aids in analyzing fractional-order PWC systems.

Set-valued analysis and differential inclusions are effective tools for this study.

Abstract

In this paper, a continuous approximation to studying a class of PWC systems of fractionalorder is presented. Some known results of set-valued analysis and differential inclusions are utilized. The example of a hyperchaotic PWC system of fractional order is analyzed. It is found that without equilibria, the system has hidden attractors.