General multi-switching synchronization using sliding mode control

Chaotic synchronization is a self-organizing phenomenon that occurs when two or more chaotic systems become synchronized. So far for multi-switching synchronization (MSS), only a homogeneous kind of switches have been discussed. This paper presents a generalized approach to MSS in which all possible heterogeneous combinations are presented. This generalization of MSS allows for greater flexibility and robustness in the MSS process. The switches are designed based on the order of the drive/response subsystems. The author also uses sliding mode control to achieve synchronization among various heterogeneous combinations during MSS. To demonstrate the effectiveness of the proposed approach, the author uses the Lorenz hyper chaotic system (LHCS) and the Chen hyper chaotic system (CHCS). The four different heterogeneous types of switches are designed and demonstrated for the chosen hyper chaotic systems. Mathematica is used for all numerical simulations. The results show that the proposed approach can achieve synchronization between two hyper chaotic systems with high accuracy. The author also shows that the proposed approach is robust to change in the parameters of the systems. This paper provides a new approach to chaotic synchronization that has potential applications in a variety of fields. The results presented in this paper are an important step towards the development of more robust and flexible synchronization schemes.