Adaptive Control and Synchronization of Hyperchaotic Cai System

The hyperchaotic Cai system (Wang, Cai, Miao and Tian, 2010) is one of the important paradigms of fourdimensional hyperchaotic systems. This paper investigates the adaptive control and synchronization of hyperchaotic Cai system with unknown parameters. First, adaptive control laws are designed to stabilize the hyperchaotic Cai system to its unstable equilibrium point at the origin based on the adaptive control theory and Lyapunov stability theory. Then adaptive control laws are derived to achieve global chaos synchronization of identical hyperchaotic Cai systems with unknown parameters. Numerical simulations are shown to demonstrate the effectiveness of the proposed adaptive control and synchronization scheme