Identical and Nonidentical Synchronization of Hyperchaotic Systems by Active Backstepping Method

This paper focuses on the tracking and synchronization problems of hyperchaotic systems based on active backstepping method. The method consists of a recursive approach that interlaces the choice of a Lyapunov function with the design of feedback control. First, a nonlinear recursive active backstepping control vector is designed to track any desired trajectory in hyperchaotic Wang system. Furthermore, this method is applied to achieve hyperchaos synchronization of two identical hyperchaotic Wang systems. Also, it is used to implement global asymptotic synchronization between hyperchaotic Wang system and hyperchaotic Rössler system. Numerical simulations have been employed to verify the effectiveness of the three designed active backstepping control vectors.