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Stability analysis of stochastic functional differential equations with infinite delay and its application to recurrent neural networks. (English) Zbl 1193.34168

Summary: We investigate the stochastic functional differential equations with infinite delay. Some sufficient conditions are derived to ensure the \(p\)th moment exponential stability and \(p\)th 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 \(p\)th 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.

MSC:

34K50 Stochastic functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
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