Stability Analysis Of Stochastic Cohen-Grossberg Neural Networks

Cohen-Grossberg neural networks were originally proposed by Cohen and Grossberg in 1983,the Cohen-Grossberg neural networks model includes many well-known models in such disciplines as population biology,neurobiology,evo-lutionary theory.Owing to the practical application in pattern recognition,associative memory,signal processing,image processing,combinatorial opti-mization,so,attracts an increasing number of scholars focus.However,in real systems,Cohen-Grossberg neural networks are often effect by random perturbed,impulses,Markov switching,which may destruction the stability of the systems.Therefore,it is important to focus on the stability criteria for the equilibrium solutions of stochastic Cohen-Grossberg neural network-s.In this dissertation,the problem stability of stochastic Cohen-Grossberg neural networks are investigated systematically.Some important theorem-s and corollaries are obtained for stochastic asymptotic stability and almost sure exponential stability of stochastic Cohen-Grossberg 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 and preliminary knowledge.2.Concerned with the problem for stochastic asymptotic stability of s-tochastic Cohen-Grossberg neural networks with Markov switching and no Markov switching.By constructing Lyapunov function,using stochastic anal-ysis techniques and Ito differential formula,several novel sufficient conditions are obtained to ensure the stochastic asymptotic stability.3.The almost sure exponential stability for stochastic Cohen-Grossberg neural networks with impulses is discussed.the criteria for almost sure expo-nential stability are given of linear and nonlinear systems.Finally,the given an example and their simulations shows that the method is effective.4.Focused on the problem of almost sure exponential stability analysis of impulsive stochastic Cohen-Grossberg neural networks with Markov switch-ing.A set of sufficient conditions of almost sure exponential stability is given by using average impulsive interval approach.Then,an example is given to illustrate the effectiveness of the results obtained.Finally,the main results of the dissertation are concluded and some issues for future research are proposed.