On multistability behavior of Unstable Dissipative Systems

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.