Dynamic Analysis Of Stochastic Delayed Systems

In this paper,the dynamic behaviors of two classes of stochastic delayed systems are studied by using Lyapunov functional method and stochastic analysis theory,the main statement of this work is as follows:In Chapter 1,the research background,research progress and practical significance of stochastic delayed systems are introduced,at the same time,the related definitions and lemmas are given.In Chapter 2,a class of stochastic delayed one-predator and two-competing-prey systems with two kinds of different functional responses are investigated.By establishing appropriate Lyapunov functions,the globally positive solution and stochastic boundedness are investigated.In some case,the stochastic permanence and extinction are also obtained.Moreover,sufficient conditions of the global asymptotic stability of the system are established.Finally,some numerical examples are provided to explain our conclusions.In Chapter 3,the input-to-stability for a class of stochastic neutral-type memristive neural networks is studied.Neutral terms and mixed delays are taken into account in this system,which make the system more novel.Using the stochastic analysis theory and Lyapunov stability theory,the conditions of mean-square exponential input-to-stability for system are obtained.Furthermore,a numerical example is given to illustrate the correctness of our conclusions.In Chapter 4,the summary of the paper and the prospect of further work are given.