Coexistence of hidden attractors and self-excited attractors through breaking heteroclinic-like orbits of switched systems

TL;DR

This paper presents a method to generate and analyze systems with coexisting hidden and self-excited attractors, revealing multistability phenomena in piecewise linear switched systems.

Contribution

It introduces a novel approach to create multistable systems with both hidden and self-excited attractors through breaking heteroclinic-like orbits.

Findings

Hidden attractors emerge from rupture of heteroclinic-like trajectories.

Multistability occurs naturally in the studied class of systems.

Feasibility of geometric design for multistable systems is demonstrated.

Abstract

In this paper an approach to generate hidden attractors based on piecewise linear (PWL) systems is studied. The approach consists of the coexistence of self-excited attrators and hidden attractors, i.e., the equilibria of the system are immersed in the basin of attraction of the seft-excited attractors, so hidden attractors appear around these self-excited attractors. The approach starts by generating a double-scroll attractor based on two equilibria presented heteroclinic orbits. Then, two equilibria are added to the system, so biestability is generated by displaying two self-excited attractor. In this paper we show that hidden attractors arise as a consequence of the rupture of trajectories that resemble heteroclinic orbits at a larger scale. Therefore, multistability appears naturally as an interesting phenomenon present in this class of dynamical systems via hidden attractors and self-excited attractors. The study suggests the feasibility of the geometric design of new classes of multistable systems with coexistence of the two classes of attractors or even multistable systems without equilibria at all.