New criteria for globally exponential stability of delayed Cohen-Grossberg neural network

Authors:
Shengshuang Chen;Weirui Zhao;Yong Xu
Affiliations:
Department of Mathematics, Wuhan University of Technology, Wuhan, Hubei 430070, China;Department of Mathematics, Wuhan University of Technology, Wuhan, Hubei 430070, China and Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, China;Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, China
Venue:
Mathematics and Computers in Simulation
Year:
2009

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Abstract

This paper is concerned with analysis problem for the global exponential stability of the Cohen-Grossberg neural networks with discrete delays and with distributed delays. We first prove the existence and uniqueness of the equilibrium point under mild conditions, assuming neither differentiability nor strict monotonicity for the activation function. Then, we employ Lyapunov functions to establish some sufficient conditions ensuring global exponential stability of equilibria for the Cohen-Grossberg neural networks with discrete delays and with distributed delays. Our results are not only presented in terms of system parameters and can be easily verified and also less restrictive than previously known criteria. A comparison between our results and the previous results admits that our results establish a new set of stability criteria for delayed neural networks.