Chaos synchronization of two different hyperchaotic systems with unknown parameters

For the synchronization of two different hyperchaotic systems with unknown parameters, a novel method to design adaptive control law and a parameter update rule is proposed. Suitable controller and adaptive law of parameters are designed to realize the synchronization by the adaptive controlling method. Based on Lyapunov stability theory, it is proved that the synchronization error system is asymptotically stable and parameters estimates converge to their true value. The proposed technique is applied to achieve chaos synchronization for the hyperchaotic Chen and Lu system with unknown parameters. Numerical simulation results are presented to demonstrate the effectiveness of the method.