Passivity And Synchronization Of Randomly Coupled Neural Network

In recent years,coupled neural networks have great potential application value in many engineering fields.As is known to all,stochastic disturbances are unavoidable in the implementation of neural networks,and may cause bad dynamic behaviors in neural networks.However,when studying the dynamical behavior of coupled neural networks,only a few of the results consider the influence of stochastic perturbation.In this paper,passivity and synchronization of two kinds of neural network models under the influence of random factors are discussed.The main research work and achievements are as follows:Firstly,due to the inevitability of stochastic disturbances,the existing passive definition and neural network model are improved in this paper.On the basis of the existing definition of passivity,considering the different dimension of input and output vectors,the definitions of passivity and finite-time passivity of stochastic systems in the expected sense are given.In addition,stochastic terms are added to the neural network and complex network models,and the effects of multi-state couplings,multi-delay state couplings and time-varying delay factors are considered.Secondly,passivity and synchronization of stochastic coupled neural networks with multiple states and multiple delay states are analyzed for the first time.Firstly,by means of some lemmas and Lyapunov functional method,combined with some inequality scaling techniques,we derive and establish for the first time the sufficient conditions of passivity,strictly passivity of input and strictly passivity of output.Furthermore,based on the results of output passivity,the synchronization criterion of the network model is obtained.Finally,the validity of the theoretical results is verified by some numerical simulation examples.Thirdly,in the study of finite-time passivity and synchronization,two kinds of state feedback controllers are designed to further study the stochastic coupled complex networks with time-varying delays.By making full use of the stochastic analysis method and Lyapunov functional analysis,some sufficient conditions are obtained to ensure the finitetime passivity and synchronization of the network.Finally,the validity of the theoretical results is verified by some numerical simulation examples.