Based On Two Theories To Analyze The Dynamical Behavior Of Stochastic Neural Networks With S-type Distributed Time Delays

Artificial neural network is a kind of nonlinear system which is used to process information by simulating the human brain.Because of its widely application.^ has been focused by scholars at home and abroad. And substantial results have been achieved.Nowadays, Lyapunov method is used to study the stability of the artificial neural network system in usual. The advantages are direct and effective. Thus, the deficiency is the needs of high technology. The fixed point theory method for the study of artificial neural network dynamic behavior is simple.And the algebraic criterion is easy to verify. But the process is complicated.Based on the previous literature, two methods are used to analyze the dynamic behavior of stochastic neural networks with S-type distributed delays in this paper.The main contents are as follows:The exponential stability in mean square of the stochastic higher-order Hopfield-type neural networks with S-type distributed time delays is investigated by using the Lyapunov functional method and stochastic analysis techniques. A criterion of exponential stability in the mean square is given. And an example is given to show the validity of the conclusions. Next,the well-posedness and the mean square exponential attraction of the stochastic neural networks with S-type distributed delays is focused by using fixed points theory and inequality techniques. And some conditions which are easy to verify are obtained.’Furthermore, the well-posedness and the mean square exponential attraction of the stochastic neutral-type neural networks with S-type distributed delays is focused by using Krasnoselskii fixed points theory.The criteria which are easily checked are presented. Finally, research contents are summarized and prospects of the research are given.