Section With Markov Switching Parameters And Random Impulse Neural Networks

A large classes of artificial neural networks have variable structures subject to random changes, which mainly result from the abrupt phenomena such as component and interconnection failures or random communication delays. Because local couples of the real network nodes have different ways, these make the system difficult to achieve the global synchronization, but the system can achieve the partial synchronization. Partial synchronization is a kind of synchronous cluster that some symmetrical nodes in a network appear to be synchronous, when the coupling strength of a network is within a certain scope.In many practical cases, artificial neural networks are characterized by the fact that these experience a change of state abruptly at certain instants, namely impulsive phenomenon. According to the impulsive influence of effect on network performance, there are two types of impulses:synchronizing impulses and desynchronizing impulses. In previous literatures, all of the results are investigated these two kinds of impulses separately. Based on introducing the average impulsive interval, the sufficient conditions are established to guarantee partial synchronization for the impulsive stochastic artificial neural networks with Markov switching parameter. The main contents of this dissertation are as listed follows:In chapter one, we introduce background and significance of studying the partial synchronization of impulsive artificial neural networks with time-delay, partial synchronization of the systems and Markov switching systems. And then we introduce the latest progress in investigation for stochastic artificial neural networks with Markov switching parameter. The main contributions of this thesis are shown in this part as well.In chapter two, we begin with the model of impulsive stochastic artificial neural networks with Markov switching parameter and the definition of average impulsive interval. To establish the sufficient conditions of partial synchronization for the impulsive stochastic artificial neural networks with Markov switching parameter, we firstly construct a new Lyapunov-Krasovskii function. Then some techniques are adopted to make the system node’s synchronization. Finally, numerical examples are given to show the validity of the proposed methods.In chapter three, we further study the model of impulsive stochastic artificial neural networks with Markov switching parameter include both discrete time delays and noise perturbations. Based on Lyapunov theory and the properties of Dini derivative, the sufficient conditions of partial synchronization for impulsive stochastic artificial neural networks with Markov switching parameter are established. Finally, numerical examples are given to demonstrate the effectiveness of the obtained results.