Hybrid Synchronization of LIU and LU Chaotic Systems via Adaptive Control

摘要

This paper derives new results for the hybrid synchronization of identical Liu systems, identical L¨1 systems, and non-identical Liu and L¨1 systems via adaptive control method. Liu system (Liu et al. 2004) and L¨1 system (L¨1 and Chen, 2002) are important models of three-dimensional chaotic systems. Hybrid synchronization of the three-dimensional chaotic systems addressed in this paper is achieved through the synchronization of the first and last pairs of states and anti-synchronization of the middle pairs of the two systems. Adaptive control method is deployed in this paper for the general case when the system parameters are unknown. Sufficient conditions for hybrid synchronization of identical Liu systems, identical L¨1 systems and non-identical Liu and L¨1 systems are derived via adaptive control theory and Lyapunov stability theory. Since the Lyapunov exponents are not needed for these calculations, the adaptive control method is very effective and convenient for the hybrid synchronization of the chaotic systems addressed in this paper. Numerical simulations are shown to illustrate the effectiveness of the proposed synchronization schemes