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Mean square exponential stability and periodic solutions of stochastic delay cellular neural networks

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  • Lu, Jun-Xiang
  • Ma, Yichen

Abstract

This paper mainely concerns the exponential stability analysis and the existence of periodic solution problems for a class of stochastic cellular neural networks with discrete delays (SDCNNs). Above all, Poincare contraction theory is utilized to derive the conditions guaranteeing the existence of periodic solutions of SDCNNs. Next, Lyapunov function, stochastic analysis theory and Young inequality approach is developed to derive some theorems which gives several sufficient conditions such that periodic solutions of SDCNNs are mean square exponential stable. These sufficient conditions only including those governing parameters of SDCNNs can be easily checked by simple algebraic methods. Finally, two examples are given to demonstrate that the proposed criteria are useful and effective.

Suggested Citation

  • Lu, Jun-Xiang & Ma, Yichen, 2008. "Mean square exponential stability and periodic solutions of stochastic delay cellular neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1323-1331.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:5:p:1323-1331
    DOI: 10.1016/j.chaos.2007.08.053
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    References listed on IDEAS

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    1. Wang, Zidong & Lauria, Stanislao & Fang, Jian’an & Liu, Xiaohui, 2007. "Exponential stability of uncertain stochastic neural networks with mixed time-delays," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 62-72.
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    Cited by:

    1. Zhifu Jia & Cunlin Li, 2023. "Almost Sure Exponential Stability of Uncertain Stochastic Hopfield Neural Networks Based on Subadditive Measures," Mathematics, MDPI, vol. 11(14), pages 1-19, July.
    2. Wang, Fengyan & Wang, Xiaoyi & Zhang, Shuwen & Ding, Changming, 2014. "On pulse vaccine strategy in a periodic stochastic SIR epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 66(C), pages 127-135.
    3. Huang, Zaitang & Yang, Qi-Gui, 2009. "Existence and exponential stability of almost periodic solution for stochastic cellular neural networks with delay," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 773-780.
    4. Feng, Wei & Yang, Simon X. & Wu, Haixia, 2009. "On robust stability of uncertain stochastic neural networks with distributed and interval time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2095-2104.
    5. Senan, Sibel & Arik, Sabri, 2009. "New results for global robust stability of bidirectional associative memory neural networks with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2106-2114.

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