Stability of impulsive stochastic differential delay systems and its application to impulsive stochastic neural networks

Abstract

This paper is concerned with the stability of n -dimensional stochastic differential delay systems with nonlinear impulsive effects. First, the equivalent relation between the solution of the n -dimensional stochastic differential delay system with nonlinear impulsive effects and that of a corresponding n -dimensional stochastic differential delay system without impulsive effects is established. Then, some stability criteria for the n -dimensional stochastic differential delay systems with nonlinear impulsive effects are obtained. Finally, the stability criteria are applied to uncertain impulsive stochastic neural networks with time-varying delay. The results show that, this convenient and efficient method will provide a new approach to study the stability of impulsive stochastic neural networks. Some examples are also discussed to illustrate the effectiveness of our theoretical results.