Dynamical Behavior Analysis Of Stochastic Neural Networks With S-type Distributed Delays

Artificial neural network is a kind of nonlinear information processing systemwhich is used to achieve certain intelligent behaviors by simulating the human brainstructure. It has been widely applied in pattern recognition, image processing,financial forecasting, signal processing, automatic control, decision support, artificialintelligence and many other fields. Because the signal transmission process is affectedby human factors, random signals and technical level and other objective factors, timedelays and random phenomenon is inevitable. Recently, many results have beenreported for stochastic neural networks with discrete and distributed delays. But theresults of stochastic neural networks with S-distributed delays are rare. Moreover, thesystems with discrete and distributed delays are independent of each other, the systemwith S-distributed delays contains them. Therefore, it is not only the need of theorybut also the need of application of the studying of stochastic neural networks withS-distributed delays.Based on the previous literature, this paper discusses the dynamical behavior ofseveral classes of stochastic neural network with S-type distributed delays. The maincontents are shown as follows:Firstly, the research background of artificial neural networks and stochasticdynamical system are introduced. Then, the exponential stability in mean square isdiscussed for stochastic Cohen-Grossberg-type BAM neural networks with S-typedistributed delays, and a stability criterion is obtained by using Lyapunov functionalmethod and stochastic analysis techniques. A few results of related literatures isextended. Furthermore, the exponential synchronization in mean square is discussedfor stochastic BAM neural networks with S-type distributed delays by Ito formulaand functional method，and a sufficient condition is given to ensure exponential synchronization of the system. Finally, the exponential synchronization in meansquare is discussed for stochastic neural networks whose diffusion coefficientcontains S-type distributed delays，and a stability criterion is obtained by usinginequality technique and functional method. A few results of related literatures isextended. In addition, We also give a summary and outlook.