Almost Sure Exponential Stability Analysis Of Stochastic Neural Networks

The wide application of neural networks in many disciplines attracts an increasing number of scholars' focus.However,both stochastic perturbation and impulses affect the real system inevitably and may destroy its stability.Therefore,it is important to focus on the stability criteria for the equilibrium solutions of stochastic neural networks.In this dissertation,the problem of stochastic neural networks and impulsive stochastic neural networks are in-vestigated systematically.Some important theorems are obtained for almost sure exponential stability of stochastic neural networks and impulsive stochas-tic neural networks by contracting Lyapunov function,using Ito differential formula,some stochastic analysis techniques and combing the linear matrix inequalities.The dissertation is mainly made up of the following parts:1.An introduction to the background and significance of stochastic neural networks in the preface are given.Then,the research progress in the stability of stochastic neural networks are reviewed briefly.2.The almost sure exponential stability for a class of stochastic neural networks is discussed.Firstly,the theorem are established in terms of lin-ear matrix inequalities for almost sure exponential stability of m-dimension stochastic neural networks based on Lyapunov stability theory,using stochas-tic analysis techniques and Ito differential formula.Secondly,on the basis of stability analysis,the criteria for almost sure exponential stability of m-dimension uncertain stochastic neural networks are derived combing some in-equalities techniques.At last,the given numerical example shows that the method is effective.3.Consider a more realistic mathematical model:a class of stochastic neu-ral networks with impulses.Firstly,the definition of almost sure exponential stability of impulsive stochastic neural networks is given.Then,some almost sure exponential stability criteria for impulsive stochastic neural networks are expressed based on Lyapunov function method,martingale exponential in-equalities and Borel-Cantelli lemma.At last,the example with numerical is given to illustrate the effectiveness of the obtained results.Finally,the main results of the dissertation are concluded and some issues for future research are proposed.