Emergence of Hidden Attractors through the Rupture of Heteroclinic-Like Orbits of Switched Systems with Self-Excited Attractors

Abstract

"This work is dedicated to the study of an approach that allows the generation of hidden attractors based on a class of piecewise-linear (PWL) systems. The systems produced with the approach present the coexistence of self-excited attractors and hidden attractors such that hidden attractors surround the self-excited attractors. The first part of the approach consists of the generation of self-excited attractors based on pairs of equilibria with heteroclinic orbits. Then, additional equilibria are added to the system to obtain a bistable system with a second self-excited attractor with the same characteristics. It is conjectured that a necessary condition for the existence of the hidden attractor in this class of systems is the rupture of the trajectories that resemble heteroclinic orbits that join the two regions of space that surround the pairs of equilibria; these regions resemble equilibria when seen on a larger scale. With the appearance of a hidden attractor, the system presents a multistable behavior with hidden and self-excited attractors."