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Exponential Stability of Impulsive Delayed Reaction‐Diffusion Cellular Neural Networks via Poincaré Integral Inequality

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  • Xianghong Lai
  • Tianxiang Yao

Abstract

This work is devoted to the stability study of impulsive cellular neural networks with time‐varying delays and reaction‐diffusion terms. By means of new Poincaré integral inequality and Gronwall‐Bellman‐type impulsive integral inequality, we summarize some novel and concise sufficient conditions ensuring the global exponential stability of equilibrium point. The provided stability criteria are applicable to Dirichlet boundary condition and show that not only the reaction‐diffusion coefficients but also the regional features including the boundary and dimension of spatial variable can influence the stability. Two examples are finally illustrated to demonstrate the effectiveness of our obtained results.

Suggested Citation

  • Xianghong Lai & Tianxiang Yao, 2013. "Exponential Stability of Impulsive Delayed Reaction‐Diffusion Cellular Neural Networks via Poincaré Integral Inequality," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:131836
    DOI: 10.1155/2013/131836
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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. Yutian Zhang, 2012. "Asymptotic Stability of Impulsive Reaction-Diffusion Cellular Neural Networks with Time-Varying Delays," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, November.
    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. Yutian Zhang, 2012. "Asymptotic Stability of Impulsive Reaction‐Diffusion Cellular Neural Networks with Time‐Varying Delays," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
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