Chaotic dynamics of three-dimensional piecewise linear systems with sliding heteroclinic cycles

Abstract

This paper explores chaotic dynamics in a class of three-dimensional piecewise linear systems with sliding heteroclinic cycles which are composed of two sliding heteroclinic orbits connecting two saddle-foci or a saddle-focus and a saddle. The system with a sliding heteroclinic cycle connecting two saddle-foci has infinite chaotic invariant sets under an eigenvalue condition, while the existence of chaotic invariant sets for the system with a sliding heteroclinic cycle connecting a saddle-focus and a saddle needs an additional condition except for an eigenvalue condition.