Research On Dynamical Behavior Of A Class Of Stochastic Neural Networks With Time Delays

In this paper，the author studies the dynamical behaviors of a class of stochasticfunctional differential equations， the models contain stochastic cellular neuralnetworks with time delays，stochastic neutral-type neural networks，stochastic staticneural networks with time delays. The author investigates the existence and stabilityof the equilibrium，the existence and stability of periodic solutions and almost periodicsolutions.This paper is composed of six chapters and main results are described as follows:First，by employing the formula for the variation of parameters and theGronwall’s lemma，the stability of a class of stochastic differential equation withconstant delays is investigated. Also，by applying stochastic analysis approaches andsemimartingale convergence theorem，the exponential stability in the mean square andthe almost sure exponential stability of a class of stochastic differential equation withvariable delays is studied，some sufficient conditions are derived.Second，by applying the properties of the M-matrix，the theory of topologicaldegree，the global stochastic asymptotic stability for stochastic cellular neuralnetworks. By using the stochastic analysis technique and Lyapunov stability theory，the global exponential robust stability of stochastic interval cellular neural networkswith S-type distributed delays is investigated. Furthermore，the problem of existenceof square mean almost periodic solutions for stochastic impulsive cellular neuralnetworks with mixed time delays is studied，by establishing the equivalent relationbetween the given stochastic impulsive delay equation and a corresponding stochasticdelay equation without impulsive effects and utilizing the Holder’s inequality，fixedpoints principle，some new criteria are given to ensure the existence and uniqueness ofa square mean almost periodic solution.Third，based on linear matrix inequality technique，by utilizing the Lyapunov functional，the robust stability for a class of uncertain neutral-type nonlinear stochasticdelayed neural networks and a class of neutral-type impulsive stochastic neuralnetworks with mixed time delays is investigated. Numerical examples are given toillustrate the applicability of the results.Fourth，by using Banach theorem and LaSalle invariant principle，the globalrobust stability for a class of static recurrent neural networks with time-varying delaysis studied．Then，the author investigates the stability of a class of stochastic staticneural networks with variable time delays，some new criteria are derived. Finally，byestablishing an L-operator differential inequality with impulses and using theM-matrix theory and Poincare contraction theory，the problem of existence and globalexponential stability of periodic solutions for stochastic impulsive static neuralnetworks is considered，some new sufficient conditions are obtained. Moreover, theexponential convergence rate index is estimated.Finally，the main results of this paper are summarized briefly，furthermore，someresearch prospects are also proposed.