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Novel stability criteria for impulsive delayed reaction–diffusion Cohen–Grossberg neural networks via Hardy–Poincarè inequality

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  • Zhang, Yutian
  • Luo, Qi

Abstract

This work is devoted to the investigation of stability theory for impulsive delayed reaction–diffusion Cohen–Grossberg neural networks with Dirichlet boundary condition. By means of Hardy–Poincarè inequality and Gronwall–Bellman-type impulsive integral inequality, we summarize some new and concise sufficient conditions ensuring global exponential stability of the equilibrium point. The presented stability criteria show that not only reaction–diffusion coefficients but also regional features as well as the first eigenvalue of the Dirichlet Laplacian will impact the stability. In conclusion, two examples are illustrated to demonstrate the effectiveness of our obtained results.

Suggested Citation

  • Zhang, Yutian & Luo, Qi, 2012. "Novel stability criteria for impulsive delayed reaction–diffusion Cohen–Grossberg neural networks via Hardy–Poincarè inequality," Chaos, Solitons & Fractals, Elsevier, vol. 45(8), pages 1033-1040.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:8:p:1033-1040
    DOI: 10.1016/j.chaos.2012.05.001
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    References listed on IDEAS

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    1. Wang, Xiaohu & Xu, Daoyi, 2009. "Global exponential stability of impulsive fuzzy cellular neural networks with mixed delays and reaction-diffusion terms," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2713-2721.
    2. Song, Qiankun & Wang, Zidong, 2008. "Stability analysis of impulsive stochastic Cohen–Grossberg neural networks with mixed time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3314-3326.
    3. 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.
    4. Chen, Zhang & Ruan, Jiong, 2007. "Global dynamic analysis of general Cohen–Grossberg neural networks with impulse," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1830-1837.
    5. Xu, Liguang & Xu, Daoyi, 2009. "Exponential p-stability of impulsive stochastic neural networks with mixed delays," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 263-272.
    6. Huang, Tingwen & Li, Chuandong & Chen, Goong, 2007. "Stability of Cohen–Grossberg neural networks with unbounded distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 992-996.
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    Cited by:

    1. Hu, Dandan & Tan, Jieqing & Shi, Kaibo & Ding, Kui, 2022. "Switching synchronization of reaction-diffusion neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).

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