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Dynamical Behaviors of the Stochastic Hopfield Neural Networks with Mixed Time Delays

Author

Listed:
  • Li Wan
  • Qinghua Zhou
  • Zhigang Zhou
  • Pei Wang

Abstract

This paper investigates dynamical behaviors of the stochastic Hopfield neural networks with mixed time delays. The mixed time delays under consideration comprise both the discrete time‐varying delays and the distributed time‐delays. By employing the theory of stochastic functional differential equations and linear matrix inequality (LMI) approach, some novel criteria on asymptotic stability, ultimate boundedness, and weak attractor are derived. Finally, a numerical example is given to illustrate the correctness and effectiveness of our theoretical results.

Suggested Citation

  • Li Wan & Qinghua Zhou & Zhigang Zhou & Pei Wang, 2013. "Dynamical Behaviors of the Stochastic Hopfield Neural Networks with Mixed Time Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:384981
    DOI: 10.1155/2013/384981
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    References listed on IDEAS

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    1. Wang, Zidong & Fang, Jian’an & Liu, Xiaohui, 2008. "Global stability of stochastic high-order neural networks with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 388-396.
    2. Song, Qiankun & Zhao, Zhenjiang, 2005. "Global dissipativity of neural networks with both variable and unbounded delays," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 393-401.
    3. Lou, Xu Yang & Cui, Bao Tong, 2008. "Global robust dissipativity for integro-differential systems modeling neural networks with delays," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 469-478.
    4. Zhao, Hongyong & Ding, Nan & Chen, Ling, 2009. "Almost sure exponential stability of stochastic fuzzy cellular neural networks with delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1653-1659.
    5. Zhao, Hongyong & Ding, Nan, 2007. "Dynamic analysis of stochastic bidirectional associative memory neural networks with delays," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1692-1702.
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