Stability Analysis Of Several Types Of Stochastic Time-delay Neural Networks

Stability theory has been widely used.For example,natural science,engineering technology,environmental ecology,social economy,etc.In this paper,we mainly discuss the stability of several kinds of neural networks with stochastic delay.By studying the properties of solutions of different neural network models,we obtain the conditions for judging the stability of solutions.The main contents of this paper are as follows.First of all,we investigate the stochastic Hopfield neural network model with mixed delays,which is composed of constant fixed delay and continuous distributed delay.In addition,the methods we used are Lyapunov function method,inequality method and Ito formula method.By constructing a suitable Lyapunov function and applying Ito formula to the Lyapunov function.Thus,we obtain the criteria for the mean square asymptotic stability of stochastic Hopfield neural networks with mixed delays.Then,we give an example to illustrate the main results we have obtained.Next,we discuss the almost sure exponential stability of stochastic delay cellular neural networks.By constructing a suitable Lyapunov function and according to Ito formula and semimartingale convergence theorem,we draw a conclusion which the stochastic delay cellular neural networks is almost sure exponential stable.Then,by giving an example to illustrate our result.Lastly,by using Euler approach and backward Euler approach,we consider the exponential stability of stochastic delay Hopfield neural networks with jumps on numerical solutions.Under the conditions of theoretical significance,we verify that not only Euler approach but also backward Euler approach is almost sure exponential stability.However,the range of application of Euler approach is smaller than that of backward Euler approach.Moreover,our main research tool is the discrete semimartingale convergence theorem.Again,our results are explained by an example.