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Exponential Stability for a Class of Stochastic Reaction‐Diffusion Hopfield Neural Networks with Delays

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  • Xiao Liang
  • Linshan Wang

Abstract

This paper studies the asymptotic behavior for a class of delayed reaction‐diffusion Hopfield neural networks driven by finite‐dimensional Wiener processes. Some new sufficient conditions are established to guarantee the mean square exponential stability of this system by using Poincaré’s inequality and stochastic analysis technique. The proof of the almost surely exponential stability for this system is carried out by using the Burkholder‐Davis‐Gundy inequality, the Chebyshev inequality and the Borel‐Cantelli lemma. Finally, an example is given to illustrate the effectiveness of the proposed approach, and the simulation is also given by using the Matlab.

Suggested Citation

  • Xiao Liang & Linshan Wang, 2012. "Exponential Stability for a Class of Stochastic Reaction‐Diffusion Hopfield Neural Networks with Delays," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:693163
    DOI: 10.1155/2012/693163
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Yonggui Kao & Hamid Reza Karimi, 2014. "Stability in Mean of Partial Variables for Coupled Stochastic Reaction‐Diffusion Systems on Networks: A Graph Approach," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Xiaoai Li, 2014. "Existence and Exponential Stability of Solutions for Stochastic Cellular Neural Networks with Piecewise Constant Argument," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    3. 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).
    4. 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).
    5. 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).
    6. Chunge Lu & Linshan Wang, 2014. "Robust Exponential Stability of Impulsive Stochastic Neural Networks with Leakage Time‐Varying Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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