## Journal of Applied Mathematics

### Stability Analysis for Impulsive Stochastic Reaction-Diffusion Differential System and Its Application to Neural Networks

Yanke Du, Yanlu Li, and Rui Xu

#### Abstract

This paper is concerned with the stability of impulsive stochastic reaction-diffusion differential systems with mixed time delays. First, an equivalent relation between the solution of a stochastic reaction-diffusion differential system with time delays and impulsive effects and that of corresponding system without impulses is established. Then, some stability criteria for the stochastic reaction-diffusion differential system with time delays and impulsive effects are derived. Finally, the stability criteria are applied to impulsive stochastic reaction-diffusion Cohen-Grossberg neural networks with mixed time delays, and sufficient conditions are obtained for the exponential $p$-stability of the zero solution to the neural networks. An example is given to illustrate the effectiveness of our theoretical results. The systems we studied in this paper are more general, and some existing results are improved and extended.

#### Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 785141, 12 pages.

Dates
First available in Project Euclid: 14 March 2014

https://projecteuclid.org/euclid.jam/1394808103

Digital Object Identifier
doi:10.1155/2013/785141

Mathematical Reviews number (MathSciNet)
MR3094905

Zentralblatt MATH identifier
06950867

#### Citation

Du, Yanke; Li, Yanlu; Xu, Rui. Stability Analysis for Impulsive Stochastic Reaction-Diffusion Differential System and Its Application to Neural Networks. J. Appl. Math. 2013 (2013), Article ID 785141, 12 pages. doi:10.1155/2013/785141. https://projecteuclid.org/euclid.jam/1394808103

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