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Global exponential stability and periodicity of reaction–diffusion recurrent neural networks with distributed delays and Dirichlet boundary conditions

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  • Lu, Jun Guo
  • Lu, Lin Ji

Abstract

In this paper, global exponential stability and periodicity of a class of reaction–diffusion recurrent neural networks with distributed delays and Dirichlet boundary conditions are studied by constructing suitable Lyapunov functionals and utilizing some inequality techniques. We first prove global exponential convergence to 0 of the difference between any two solutions of the original neural networks, the existence and uniqueness of equilibrium is the direct results of this procedure. This approach is different from the usually used one where the existence, uniqueness of equilibrium and stability are proved in two separate steps. Secondly, we prove periodicity. Sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the equilibrium and periodic solution are given. These conditions are easy to verify and our results play an important role in the design and application of globally exponentially stable neural circuits and periodic oscillatory neural circuits.

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  • Lu, Jun Guo & Lu, Lin Ji, 2009. "Global exponential stability and periodicity of reaction–diffusion recurrent neural networks with distributed delays and Dirichlet boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1538-1549.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:4:p:1538-1549
    DOI: 10.1016/j.chaos.2007.06.040
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    References listed on IDEAS

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    1. Cui, Bao Tong & Lou, Xu Yang, 2006. "Global asymptotic stability of BAM neural networks with distributed delays and reaction–diffusion terms," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1347-1354.
    2. Cao, Jinde & Ho, Daniel W.C., 2005. "A general framework for global asymptotic stability analysis of delayed neural networks based on LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1317-1329.
    3. Lu, Jun Guo, 2008. "Global exponential stability and periodicity of reaction–diffusion delayed recurrent neural networks with Dirichlet boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 116-125.
    4. Wang, Jian & Lu, Jun Guo, 2008. "Global exponential stability of fuzzy cellular neural networks with delays and reaction–diffusion terms," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 878-885.
    5. Li, Yongkun, 2005. "Global exponential stability of BAM neural networks with delays and impulses," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 279-285.
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    Cited by:

    1. Li, Zuoan & Li, Kelin, 2009. "Stability analysis of impulsive fuzzy cellular neural networks with distributed delays and reaction-diffusion terms," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 492-499.

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