Stability analysis of stochastic functional differential equations with infinite delay and its application to recurrent neural networks

Authors:
Xiaodi Li;Xilin Fu
Affiliations:
School of Mathematical Sciences, Xiamen University, Xiamen, 361005, PR China;School of Mathematical Sciences, Shandong Normal University, Jinan, 250014, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

In this paper, we investigate the stochastic functional differential equations with infinite delay. Some sufficient conditions are derived to ensure the pth moment exponential stability and pth moment global asymptotic stability of stochastic functional differential equations with infinite delay by using Razumikhin method and Lyapunov functions. Based on the obtained results, we further study the pth moment exponential stability of stochastic recurrent neural networks with unbounded distributed delays. The result extends and improves the earlier publications. Two examples are given to illustrate the applicability of the obtained results.