Electron. J. Diff. Equ., Vol. 2010(2010), No. 42, pp. 1-11.

Stochastic stability of Cohen-Grossberg neural networks with unbounded distributed delays

Ping Chen, Chuangxia Huang, Xiaolin Liang

Abstract:
In this article, we consider a model that describes the dynamics of Cohen-Grossberg neural networks with unbounded distributed delays, whose state variable are governed by stochastic non-linear integro-differential equations. Without assuming the smoothness, monotonicity and boundedness of the activation functions, by constructing suitable Lyapunov functional, employing the semi-martingale convergence theorem and some inequality, we obtain some sufficient criteria to check the almost exponential stability of networks.

Submitted December 21, 2009. Published March 26, 2010.
Math Subject Classifications: 34F05, 93E15.
Key Words: Cohen-Grossberg neural networks; stochastic; distributed delays; almost sure exponential stability; Lyapunov functional.

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Ping Chen
College of Mathematics and Computing Science
Changsha University of Science and Technology
Changsha, Hunan 410114, China
email: chenping04@gmail.com
Chuangxia Huang
College of Mathematics and Computing Science
Changsha University of Science and Technology
Changsha, Hunan 410114, China
email: huangchuangxia@sina.com.cn
Xiaolin Liang
College of Mathematics and Computing Science
Changsha University of Science and Technology
Changsha, Hunan 410114, China
email: liang@csust.edu.cn

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