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

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  • Chen, Shengshuang
  • Zhao, Weirui
  • Xu, Yong

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.

Suggested Citation

  • Chen, Shengshuang & Zhao, Weirui & Xu, Yong, 2009. "New criteria for globally exponential stability of delayed Cohen–Grossberg neural network," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1527-1543.
    • Handle: RePEc:eee:matcom:v:79:y:2009:i:5:p:1527-1543
    DOI: 10.1016/j.matcom.2008.07.002
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    References listed on IDEAS

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    1. Mohamad, S. & Gopalsamy, K., 2000. "Dynamics of a class of discrete-time neural networks and their continuous-time counterparts," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 53(1), pages 1-39.
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    Cited by:

    1. Zhang, Zhongjie & Yu, Tingting & Zhang, Xian, 2022. "Algebra criteria for global exponential stability of multiple time-varying delay Cohen–Grossberg neural networks," Applied Mathematics and Computation, Elsevier, vol. 435(C).

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