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New global exponential stability result to a general Cohen–Grossberg neural networks with multiple delays

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Abstract

In this paper, we first discuss the existence of an equilibrium point to a general Cohen–Grossberg neural networks with multiple delays by means of using degree theory and linear matrix inequality (LMI) technique. Then by applying the existence result of an equilibrium point, linear matrix inequality technique and constructing a Lyapunov functional, we study the global exponential stability of equilibrium solution to the Cohen–Grossberg neural networks. Compared with known results, our results of global exponential stability of equilibrium point are new. In our results, the hypothesis for differentiability in existing papers on the behaved functions is removed and the hypotheses for boundedness and monotonicity in existing papers on the activation functions are also removed.

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Authors and Affiliations

  1. College of Mathematics, Hunan University, Changsha, 410082, P.R. China

    Zhengqiu Zhang, Taipo Zhang & Ping Xiao

  2. College of Information Science and Engineering, Hunan University, Changsha, 410082, P.R. China

    Shengye Huang

Authors
  1. Zhengqiu Zhang
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  2. Taipo Zhang
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  3. Shengye Huang
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  4. Ping Xiao
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Correspondence to Zhengqiu Zhang.

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Zhang, Z., Zhang, T., Huang, S. et al. New global exponential stability result to a general Cohen–Grossberg neural networks with multiple delays. Nonlinear Dyn 67, 2419–2432 (2012). https://doi.org/10.1007/s11071-011-0156-6

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  • DOI: https://doi.org/10.1007/s11071-011-0156-6

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