On multistability behavior of Unstable Dissipative Systems

TL;DR

This paper introduces a piecewise linear system based on unstable dissipative systems that exhibits multistability and multiscroll chaotic trajectories, depending on initial conditions and parameter settings.

Contribution

It proposes a new structure for PWL systems derived from UDS that demonstrates multistability and multiscroll chaos based on parameter variation.

Findings

The PWL system can exhibit multistable behavior with multiple attractors.

Parameter ranges for multistability are identified.

The system generates chaotic multiscroll trajectories.

Abstract

We present a dissipative system with unstable dynamics called unstable dissipative system which are capable of generating a multi-stable behavior, i.e., depending on its initial condition the trajectory of the system converge to a specific basin of attraction. A piecewise linear (PWL) systems is generated based on unstable dissipative systems (UDS) whose main attribute when they are switched is the generation of chaotic trajectories with multiple wings or scrolls. For this PWL system a structure is proposed where both the linear part and the switching function depend on two parameters. We show the range of values of such parameters where the PWL system presents a multistable behavior and trajectories with multiscrolls.