Global Synchronization Of N Different Coupled Chaotic Systems With Ring And Chain Connection

Chaos synchronization, as an extremely important research in nonlinear science, is stated briefly in the article. The definition and classification of chaos synchronization together with the methods which are used to realize it is also described in details. Meanwhile, the actual value in daily life and its huge application prospects are also commented. A method is proposed to realize synchronization of N different coupled chaotic systems with ring and chain connection. For arbitrary K different chaotic systems, a closed cycle is formed through coupling with a ring connection between their state variables. Choose any one of the K systems as the aim system, and add the controller to the remaining K-1 systems. The form of controller is designed and the area of coupling coefficient is determined based on Lyapunov stability theory, and the global synchronization of the K different coupled chaotic systems is realized. Taking the new system, the Chen system and the Lüsystem as examples, numerical simulations and theoretical analysis show that the method is effective and feasible, also it can be widely used in practice. Furthermore, the method is developed into N (N>K)d ifferent chaotic systems with ring and chain connection. The controller is designed by coupling the state variables of the systems on the chain and those on the ring. All the systems on the chain can be synchronized by any of those on the ring, which shows that the synchronization of N different chaotic systems is realized. The effectiveness and feasibility of the method is also verified by Lorenz system and Rossler system and the three systems mentioned above.