| Synchronous behavior is one of the most important dynamic characteristics of memristor neural networks(MNNs).In a practical real system,there are often exist signal transmission delay and external interference disturbance.This phenomenon is attributed to time-delay and impulsive effect.Because of the time delay in the network,the presence of the time delay,the impulse and the external controller has great influence on the synchronization behavior of neural network.Therefore,based on time-delay and external controller,a more realistic model of MNNs is established and its synchronous dynamic behavior is investigated.In this thesis,we will build the MNNs models based on two basic controllers.By selecting an appropriate Lyapunov function,and using the theory of discontinuous dynamical systems,inequality techniques and the concept of average impulse interval,the theoretical framework of the synchronization of delayed memristor neural networks(DMNNs)is constructed.Furthermore,the sufficient conditions for realizing exponential synchronization of DMNNs are given.The main contents of this thesis are as follows:(1)For the exponential synchronization problem of DMNNs under feedback control,we transform the model of DMNNs by using the concept of differential inclusion,and the theory of set-valued mapping and design a new feedback controller.Moreover,a new feedback controller is designed to realize the exponential synchronization of DMNNs.Inaddition,based on the Lyapunov stability theory and the inequality techniques,a sufficient condition is given to achieve the exponential synchronization of the DMNNs.(2)In view of the positive effects of delay-dependent impulses on the synchronization of DMNNs,a criterion for mean square synchronization criterion is derived under such a kind of impulsive effect,assuming that the impulse sequence is Marcovian and not always stable.It can be seen that the stochastic impulses play an impulsive controller role,if they are stabilizing in an“average”sense. |
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