Research On Control And Synchronization Of Chaotic Neural Network

Nonlinear science is a foundational discipline which concerns the common properties of nonlinear phenomena. Particularly, Chaos theory is one of important subdiscipline of nonlinear science. People begin to study the problems of chaos control, chaos synchronization, for the neural network has the same complex dynamics as chaotic systems. The research has studied the relative problems of chaos control, chaos synchronization and its application in cryptography using the methods of theoretical derivation and numerical simulation. The main originality in this paper can be summarized as follows:(1) The problem of two coupled neurons tracking control is discussed. A controller based on the reference signal is designed. It is proved that the controller can make the error converge to zero exponentially theoretically. Numerical results have verified the validity of the controller. The two coupled neurons can not only track any reference signal fast, but can synchronize with identical or different chaotic systems.(2) The problem of the synchronization of Chen system using a new proportional reduced-order observer design is tackled in the algebraic and differential setting. We obtain the estimates of the current states (master system) and prove the error result of the new reduce-order observe is stable asymptotically. Finally, we present a simulation to illustrate the effectiveness of the suggested approach.(3) The problem of the chaotic neural networks generalized synchronization is studied. We propose an approach based on the Lyapunov stability theory. This approach realizes the generalized synchronization between two different dimensional neural networks. Numerical examples are given to demonstrate the effectiveness of this approach.(4) The adaptive projective synchronization problem of a class of delayed neural networks is studied. Based on Lyapunov stability theory, a new controller is designed. With this new and effective method, parameter identification and projective synchronization can be achieved simultaneously. The form of the controller is simple and implemented easily. The convergence rate of the controller is very fast and the control range is very broad. Numerical simulations demonstrate the effectiveness of the proposed projective synchronization scheme.