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A new criterion to global exponential periodicity for discrete-time BAM neural network with infinite delays

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  • Zhou, Tiejun
  • Liu, Yuehua
  • Li, Xiaoping
  • Liu, Yirong

Abstract

The discrete-time bidirectional associative memory neural network with periodic coefficients and infinite delays is studied. And not by employing the continuation theorem of coincidence degree theory as other literatures, but by constructing suitable Liapunov function, using fixed point theorem and some analysis techniques, a sufficient criterion is obtained which ensures the existence and global exponential stability of periodic solution for the type of discrete-time BAM neural network. The obtained result is less restrictive to the BAM neural networks than previously known criteria. Furthermore, it can be applied to the BAM neural network which signal transfer functions are neither bounded nor differentiable. In addition, an example and its numerical simulation are given to illustrate the effectiveness of the obtained result.

Suggested Citation

  • Zhou, Tiejun & Liu, Yuehua & Li, Xiaoping & Liu, Yirong, 2009. "A new criterion to global exponential periodicity for discrete-time BAM neural network with infinite delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 332-341.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:1:p:332-341
    DOI: 10.1016/j.chaos.2007.01.113
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    References listed on IDEAS

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    1. Huang, Chuangxia & Huang, Lihong & Yuan, Zhaohui, 2005. "Global stability analysis of a class of delayed cellular neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 70(3), pages 133-148.
    2. Li, Chuandong & Liao, Xiaofeng & Zhang, Rong, 2005. "Delay-dependent exponential stability analysis of bi-directional associative memory neural networks with time delay: an LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 1119-1134.
    3. Li, Yongkun & Xing, Wenya & Lu, Linghong, 2006. "Existence and global exponential stability of periodic solution of a class of neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 437-445.
    4. Huang, Xia & Cao, Jinde & Huang, De-Shuang, 2005. "LMI-based approach for delay-dependent exponential stability analysis of BAM neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 24(3), pages 885-898.
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