Chaotic behavior of a class of discontinuous dynamical systems of fractional-order

TL;DR

This paper investigates the chaotic behavior of a specific class of discontinuous fractional-order dynamical systems by transforming, approximating, and numerically simulating them, demonstrating chaos persistence through examples.

Contribution

It introduces a method to analyze chaos in discontinuous fractional-order systems using regularization, approximation, and numerical simulation techniques.

Findings

Chaos persists in the analyzed systems.

Numerical simulations confirm chaotic behavior.

The approach can be applied to similar systems.

Abstract

In this paper the chaos persistence in a class of discontinuous dynamical systems of fractional-order is analyzed. To that end, the Initial Value Problem is first transformed, by using the Filippov regularization [1], into a set-valued problem of fractional-order, then by Cellina's approximate selection theorem [2, 3], the problem is approximated into a single-valued fractional-order problem, which is numerically solved by using a numerical scheme proposed by Diethelm, Ford and Freed [4]. Two typical examples of systems belonging to this class are analyzed and simulated.