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Stability of Impulsive Cohen‐Grossberg Neural Networks with Time‐Varying Delays and Reaction‐Diffusion Terms

Author

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  • Jinhua Huang
  • Jiqing Liu
  • Guopeng Zhou

Abstract

This work concerns the stability of impulsive Cohen‐Grossberg neural networks with time‐varying delays and reaction‐diffusion terms as well as Dirichlet boundary condition. By means of Poincaré inequality and Gronwall‐Bellman‐type impulsive integral inequality, we summarize some new and concise sufficient conditions ensuring the global exponential stability of equilibrium point. The proposed criteria are relevant to the diffusion coefficients and the smallest positive eigenvalue of corresponding Dirichlet Laplacian. In conclusion, two examples are illustrated to demonstrate the effectiveness of our obtained results.

Suggested Citation

  • Jinhua Huang & Jiqing Liu & Guopeng Zhou, 2013. "Stability of Impulsive Cohen‐Grossberg Neural Networks with Time‐Varying Delays and Reaction‐Diffusion Terms," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:409758
    DOI: 10.1155/2013/409758
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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.
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    4. Xianghong Lai & Yutian Zhang, 2012. "Fixed Point and Asymptotic Analysis of Cellular Neural Networks," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-12, August.
    5. 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.
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