Hidden chaotic attractors in fractional-order systems

TL;DR

This paper introduces a method to identify hidden chaotic attractors in fractional-order nonlinear systems, analyzing stability and employing numerical integration to explore complex dynamics in three example systems.

Contribution

It presents a novel scheme for uncovering hidden chaotic attractors in fractional-order systems, including stability analysis and numerical methods applied to three different systems.

Findings

Successfully identified hidden chaotic attractors in the example systems

Demonstrated stability analysis of equilibria in fractional-order systems

Validated the approach with numerical simulations of three systems

Abstract

In this paper, we present a scheme for uncovering hidden chaotic attrac- tors in nonlinear autonomous systems of fractional order. The stability of equilibria of fractional-order systems is analyzed. The underlying initial value problem is nu- merically integrated with the predictor-corrector Adams-Bashforth-Moulton algo- rithm for fractional-order differential equations. Three examples of fractional-order systems are considered: a generalized Lorenz system, the Rabinovich-Fabrikant system and a non-smooth Chua system.