Hyperchaotic Synchronization Of Networks Of R(?)ssler Hyperchaotic System

Resent years, chaotic synchronization has been widely explored in variety of systems including physical, chemical, ecological system. The chaotic synchronization seems to be difficult to observe in physical systems since the chaotic behavior is very sensitive to both the initial condition and noise. Pecora and Carrol [8] proposed a method ( PC method ) for synthesizing a chaotically synchronizing system. The PC method is very simple and efficient in synchronizing some chaotic systems, this kind of synchronization can be realized only under the condition that all the Lyapunov exponents of the response system under the action of the driver ( the conditional Lyapunov exponents ) are negative.However, it is very difficult to provide stably synchronization for the hyperchaotic systems with more than two positive Lyapunov exponents. In this Letter, the synchronization of two symmetrical nonlinear-coupled hyperchaotic systems is discussed. A special nonlinear-coupled term is constructed by suitable separation between linear and nonlinear terms of the chaotic system, and the phenomenon of stable chaotic synchronization can be found in a certain region of the coupled strength. We use this method in hyperchaotic synchronization of R?ssler systems. And the method can also be generalized to a form for hyperchaotic synchronization of neural networks of R?ssler systems linked by special nonlinear(or linear) coupling function. Then vary parameters in a region, observe how it works on the stability of chaotic synchronization. It is shown that the method is effective for hyperchaotic synchronization of R?ssler system by numerical calculation.