Q-S synchronization in 3D Henon-like map and generalized Henon map via a scalar controller

In this Letter, a generalized, systematic and automatic backstepping scheme is developed to investigate the Q-S synchronization of two identical 3D discrete-time dynamical systems and two different 3D discrete-time dynamical systems. With the aid of symbolic-numeric computation, we use the proposed scheme to illustrate chaos synchronization between two identical 3D generalized Henon map and Q-S synchronization between two different 3D generalized Henon map and Henon-like map via a scalar controller, respectively. Moreover numerical simulations are used to verify the effectiveness of the proposed scheme. In addition, the scheme can be also applied to investigate the tracking problem in the discrete-time systems and to generate automatically the scalar controller in computer with the aid of symbolic-numeric computation. (c) 2005 Published by Elsevier B.V.