The Stability And Synchronization Analysis For Stochastic Neural Networks

Neural network is a highly complex large-scale nonlinear dynamic system which hasrich dynamics behavior. It has broad application prospects in the combinatorialoptimization, pattern recognition, image processing, associative memory and other fieldsbecause of its nonlinear transformation characteristics and highly parallel computingcapacity. However, all of these applications are greatly dependent on the dynamiccharacteristics of the neural network. According to the views of neurophysiology,biological neurons are random in nature. Due to when neural network to accept the samerepetitive stimulation, its response is not the same. This means that the randomness in thebiological neural network plays an important role. So the stability analyses of thestochastic neural network has been research hot spot, and obtained many important results.However, the time delays are inevitable in the neural network. The time delays mayaffect the stability of the neural network system, such as generate oscillation andinstability. At present, in the stability theory of the time-delays neural network, thetime-delays neural network are mostly related to the constant delays or varying delays, butthe stability theory for the time-delays can be randomly change of the neural network isrelatively rare. So, the stability research of the time-delays stochastic neural network andsynchronous control undoubtedly has important application value.In this paper, the research of the stability and synchronization of the stochastictime-delays neural network by constructing the proper Lyapunov-Krasovskii functional,Ito formula, weak infinitesimal generator, liberty weight matrix, Jensen inequality andsliding mode control method. The main researches are as follows:First of all, the stability of the series time-delays neural network with Markovianjump parameters and random disturbance was analyzed and discussed. By constructing anew Lyapunov function, using the theory of Ito differential equation, the robustexponential stability in the sense of expects criterion was given.Secondly, for a class of generalized discrete time neural networks with uncertaintiesparameter, the regular causation and stochastic stability were studied by referencedifference equation and linear matrix inequality (LMI) theory. And then, the new theory was concluded.And then, synchronization of the time-delays node with Markovian dependentgeneralized complex network was discussed. By using the Kronecker product, Jenseninequality theory, it is concluded that the criterion of generalized complex network globalsynchronization.Finally, the projective synchronization problem of stochastic neural network wassolved by using Lyapunov-Krasovskii functional theory and infinitesimal generator. Theprojection and projection lag synchronization theory basis and the stability of the systemwas given by constructing dynamic integral sliding mode controller.