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Asymptotic Stability of Impulsive Reaction-Diffusion Cellular Neural Networks with Time-Varying Delays

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  • Yutian Zhang

Abstract

This work addresses the asymptotic stability for a class of impulsive cellular neural networks with time-varying delays and reaction-diffusion. By using the impulsive integral inequality of Gronwall-Bellman type and Hardy-Sobolev inequality as well as piecewise continuous Lyapunov functions, we summarize some new and concise sufficient conditions ensuring the global exponential asymptotic stability of the equilibrium point. The provided stability criteria are applicable to Dirichlet boundary condition and showed to be dependent on all of the reaction-diffusion coefficients, the dimension of the space, the delay, and the boundary of the spatial variables. Two examples are finally illustrated to demonstrate the effectiveness of our obtained results.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnljam:501891
    DOI: 10.1155/2012/501891
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    Cited by:

    1. Ruofeng Rao & Xiongrui Wang & Shouming Zhong & Zhilin Pu, 2013. "LMI Approach to Exponential Stability and Almost Sure Exponential Stability for Stochastic Fuzzy Markovian‐Jumping Cohen‐Grossberg Neural Networks with Nonlinear p‐Laplace Diffusion," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    2. 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).
    3. Xiongrui Wang & Ruofeng Rao & Shouming Zhong, 2012. "LMI Approach to Stability Analysis of Cohen‐Grossberg Neural Networks with p‐Laplace Diffusion," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    4. Ruofeng Rao & Zhilin Pu & Shouming Zhong & Jialin Huang, 2013. "On the Role of Diffusion Behaviors in Stability Criterion for p‐Laplace Dynamical Equations with Infinite Delay and Partial Fuzzy Parameters under Dirichlet Boundary Value," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    5. M. De la Sen, 2013. "Some Results on Fixed and Best Proximity Points of Precyclic Self‐Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).

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