Synchronization and Its Conditions for Discrete Chaotic Systems by Linear and Nonlinear Feedback

Based on the stability theory of discrete systems and Pecora Carrol chaotic synchronization theorem, the syn-chronization for a class of discrete chaotic multi variable systems is studied. A new method named linear and nonlinear feed-back control is presented. The synchronization controller includes linear and nonlinear feedback, and the response system is driven by all variables of the drive system. Through analyzing the equation of the error system and calculating the maximum Lyapunov exponents of the response system, the synchronization conditions are gained. Then, the method is applied to Henon mapping system, and the synchronization between response and drive Henon systems is realized, and the relations between synchronization performances and control parameters are discussed. The simulation based on Matlab software shows its effectiveness.