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Dynamics of Fuzzy BAM Neural Networks with Distributed Delays and Diffusion

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  • Qianhong Zhang
  • Lihui Yang
  • Jingzhong Liu

Abstract

Constructing a new Lyapunov functional and employing inequality technique, the existence, uniqueness, and global exponential stability of the periodic oscillatory solution are investigated for a class of fuzzy bidirectional associative memory (BAM) neural networks with distributed delays and diffusion. We obtained some sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the periodic solution. The results remove the usual assumption that the activation functions are differentiable. An example is provided to show the effectiveness of our results.

Suggested Citation

  • Qianhong Zhang & Lihui Yang & Jingzhong Liu, 2012. "Dynamics of Fuzzy BAM Neural Networks with Distributed Delays and Diffusion," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:136048
    DOI: 10.1155/2012/136048
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    References listed on IDEAS

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    1. Cao, Jinde & Ho, Daniel W.C., 2005. "A general framework for global asymptotic stability analysis of delayed neural networks based on LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1317-1329.
    2. Hu, Jin & Zhong, Shouming & Liang, Li, 2006. "Exponential stability analysis of stochastic delayed cellular neural network," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 1006-1010.
    3. Huang, Tingwen, 2007. "Exponential stability of delayed fuzzy cellular neural networks with diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 658-664.
    4. Zhu, Wenli & Hu, Jin, 2006. "Stability analysis of stochastic delayed cellular neural networks by LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 171-174.
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    Cited by:

    1. Xinghua Liu & Hongsheng Xi, 2013. "On Delay‐Range‐Dependent Stochastic Stability Conditions of Uncertain Neutral Delay Markovian Jump Systems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).

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