Exponential Stability Analysis For Stochastic Neural Networks And Stochastic Genetic Networks With Delays

Applications of the determinate system described by ordinary differential equationin the domain of physics, engineering technology, biology and economic system etc. arewell known. But, with development of science and technology, description on practicalproblem is required to be better and better. Therefore, e?ects of the stochastic factorscann't be neglected, and description for practical systems should be necessary to con-vert from usual determinate systems to stochastic systems. Stability is an importantdynamic characteristic and one of the main target of engineering design. The complexityof environment that practical engineering systems is in and action which is required to ac-complish are not completely same, so the paper shall go deep into the dynamic behaviorsof nonlinear stochastic systems.In this paper, by applying the method of variation parameter, inequality techniquesand conducting some stochastic analysis, the exponential stability problem is consideredrespectively for stochastic neural networks and genetic networks with time delays.The First chapter is introduction, in which we present research background, purposeand significance of stochastic neural networks and genetic networks, and then the researchstatus and results of stochastic neural networks and genetic networks are given. Finallythe organization of this paper is also presented.The related theory of stochastic di?erential equation are presented in chapter 2.In chapter 3, stochastic neural networks with time delays systems are discussed.By applying the method of variation parameter, inequality techniques and conductingsome stochastic analysis, several su?cient conditions ensuring P moment exponentialstability are obtained. Compare with the previous works, our method do not resort toany Lyapunov function, and the result derived in this paper generalize some earlier worksreported in the literature. Finally, Several examples are also given to show the usefulnessof the proposed result. The uncertain stochastic genetic networks with time discrete delays systems are in-vestigated in chapter 4, and then, by applying similar methods and introducing spectralradius, several suffcient conditions ensuring P moment exponential stability are obtained.Finally, Several examples are also given to show the usefulness of the proposed result.In chapter 5, the stochastic genetic networks with time distribute delays systems areinvestigated. Firstly, by applying method of It(?) differential and LMI, several su?cientconditions ensuring stochastic asymptotic stability are obtained. Finally, Several examplesare also given to show the usefulness of the proposed result.