Constructing Chaotic Systems from a Class of Switching Systems

This paper aims to develop an approach for constructing chaotic systems from a class of linear continuous-time switching systems. First, the Shilnikov criterion is analyzed and extended to the switching systems. Then some kinds of “swing planes” are provided via a heteroclinic loop design, which act as switching planes to chaotify the systems. Furthermore, a numerical example is presented to validate the proposed principle and implementation scheme. The theoretical analysis and numerical simulation have demonstrated the feasibility and effectiveness of the developed techniques.