The Impulsive Control And Synchronization Of Neural Networks Systems With Delays

It is well known that impulsive control and synchronization of chaos system is animportant problem in nonlinear science. Synchronization of chaotic systems has been ex-tensively studied and the research have been applying in many di?erent areas. Therefore,with the development of the society and requirement of the growth, based on the resultsin previous studies, we also need to study the synchronization of the chaotic systems moredetailed. In this paper, by constructing di?erent controllers, the exponential lag synchro-nization of a class of neural networks with mixed delays and impulsive e?ects, completesynchronization of Cohen-Grossberg neural networks with mixed time-varying delays andimpulsive e?ects as well as the adaptive synchronization of a class of unknown chaoticneural networks with time-varying delay are studied, respectively.The main contents in this paper can be summarized as follows:1. In the ?rst chapter, in which we present research background, purpose, signif-icance, some famous mathematical model and some research results of chaotic neuralnetworks and chaos control. In the end, the organization of this paper is given.2. In the second chapter, the exponential lag synchronization of a class of neuralnetworks with mixed delays and impulsive e?ects are discussed. By using the Lyapunovstability theory and the inequality analysis technique, some su?cient conditions ensuringthe globally asymptotical stability and exponential stability of chaotic system, respective-ly. And then, the exponential lag synchronization of chaos system are obtained. Finally,some numerical examples and simulations are presented to show the feasibility and e?ec-tiveness of the proposed methods.3. The complete synchronization of Cohen-Grossberg neural networks with mixedtime-varying delays and impulsive e?ects are investigated in the third chapter. By usingthe Lyapunov stability theory and the impulsive di?erential inequality method, somesu cient conditions are derived to ensure the globally exponentially stability for the chaos system. The criterion of asymptotical synchronization of chaos system are obtained.Finally, some numerical examples are presented to verify the obtained results.4. In the fourth chapter, we consider the adaptive synchronization of a class of un-known chaotic neural networks with time-varying delay. Based on the proposed model in[69] and the LaSalle invariant principle of functional di?erential equations as well as theadaptive feedback control technique, some su?cient conditions for adaptive synchroniza-tion and globally asymptotical stability of unknown delayed neural networks are obtained.Finally, some numerical examples and simulations are presented to show the feasibilityand e?ectiveness of the proposed methods.