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

被引：58

作者：

Li, Xiaodi ^{[2
]}

Fu, Xilin ^{[1
]}

机构：

[1] Shandong Normal Univ, Sch Math Sci, Jinan 250014, Peoples R China

[2] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2010年 / 234卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Stochastic functional differential equations; Stability; Infinite delay; Recurrent neural networks; Razumikhin method; Lyapunov functions; Unbounded distributed delays; RAZUMIKHIN-TYPE THEOREMS; TIME-VARYING DELAYS; EXPONENTIAL STABILITY; ASYMPTOTIC STABILITY; DISTRIBUTED DELAYS; EXISTENCE; UNIQUENESS;

D O I：

10.1016/j.cam.2009.12.033

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2010 Published by Elsevier B.V.

引用

页码：407 / 417

页数：11

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