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Zbl 1218.34097
Li, Chunxiang; Shi, Junping; Sun, Jitao
Stability of impulsive stochastic differential delay systems and its application to impulsive stochastic neural networks. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 10, 3099-3111 (2011). ISSN 0362-546X

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 2000:: *34K50 Stochastic delay equations
34K20 Stability theory of functional-differential equations
92B20 General theory of neural networks
34K45 Equations with impulses

Keywords: stability; stochastic system; delay; impulsive control; neural networks

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