Several Kinds Of Coordination Behavior Of Memristor Neural Networks

In recent years,memristor has aroused great interest from scholars at home and abroad in exploring its properties and applications from the perspective of mathematics and physics,due to its special memory,nonlinear characteristics,low power consumption,simple physical structure and good expansibility.As a nonlinear dynamic nano-device with unique memory characteristics,memristor can control the change of its resistance value through the voltage or current applied and save the value after power failure.Combined with the initial value sensitivity of chaos,more complex dynamic phenomena will be generated in the circuit,bringing new vitality to many research fields.In this paper,complex network theory,differential system theory and control theory are used to discuss several kinds of the coordination behavior of memristive neural networks respectively(including mean square exponential synchronization,quasi-synchronization and almost sure synchronization).The main contents are as follows:Firstly,the mean square synchronization problem for a class of stochastic memristor neural networks with time-varying delays is discussed in detail by using the aperiodic intermittent control strategy.The reset rate in the neural network is expressed as a unified form by applying fuzzy model,and a simple linear feedback control strategy is designed to obtain the criterion to ensure the mean square synchronization among the drive-response neural network systems.Furthermore,the adaptive control factor is introduced into the coupling term of the neural network,and then the corresponding synchronization criterion is established by using the adaptive control strategy under the given updating criterion.Then the quasi synchronization of a nonlinear coupled memristive neural network with time delay under pinning control is studied.Firstly,a nonlinear coupled memristive neural network with time-varying delays and uncertain parameters is constructed.Then by using Lyapunov function method,matrix theory and designing memristive mechanism and pinning control strategy,some sufficient conditions are obtained to ensure the drive o-response coupling memristive neural network system.In addition,the results are extended to the memristive neural network under different conditions(such as linear coupling function,adaptive coupling strength,control node proportion,etc.),and the corresponding synchronization criteria are obtained under these conditions.Finally,in view of the fact that noise is inevitable in the application of practical neural networks,the almost sure synchronization for a class of memristive neural networks with time delays and random noise is analyzed.By designing a state feedback controller and using Lyapunov stability theory,matrix theory,the stochastic differential equation theory,including Grownwall Bellman inequality,Borel Cantelli inequality,Holder inequality and Burkholder-Davis inequality,it is proved that under certain conditions the drive-response memrstive neural networks with time-varying delays can achieve almost sure synchronization.Furthermore,the corresponding results are generalized to those with m dimension random noise.In addition,considering the memristive neural network without time-varying delays,a different and simple method is proposed to realize the almost sure synchronization.