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Stability of impulsive stochastic differential delay systems and its application to impulsive stochastic neural networks. (English) Zbl 1218.34097
Summary: This paper is concerned with the stability of $n$-dimensional stochastic differential delay systems with nonlinear impulsive effects. First, an equivalence 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 $n$-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 the study of the stability of impulsive stochastic neural networks. Some examples are also discussed to illustrate the effectiveness of our theoretical results.
##### MSC:
 34K50 Stochastic functional-differential equations 34K20 Stability theory of functional-differential equations 92B20 General theory of neural networks (mathematical biology) 34K45 Functional-differential equations with impulses