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A note on exponential convergence of neural networks with unbounded distributed delays

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  • Chu, Tianguang
  • Yang, Haifeng

Abstract

This note examines issues concerning global exponential convergence of neural networks with unbounded distributed delays. Sufficient conditions are derived by exploiting exponentially fading memory property of delay kernel functions. The method is based on comparison principle of delay differential equations and does not need the construction of any Lyapunov functionals. It is simple yet effective in deriving less conservative exponential convergence conditions and more detailed componentwise decay estimates. The results of this note and [Chu T. An exponential convergence estimate for analog neural networks with delay. Phys Lett A 2001;283:113–8] suggest a class of neural networks whose globally exponentially convergent dynamics is completely insensitive to a wide range of time delays from arbitrary bounded discrete type to certain unbounded distributed type. This is of practical interest in designing fast and reliable neural circuits. Finally, an open question is raised on the nature of delay kernels for attaining exponential convergence in an unbounded distributed delayed neural network.

Suggested Citation

  • Chu, Tianguang & Yang, Haifeng, 2007. "A note on exponential convergence of neural networks with unbounded distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1538-1545.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:5:p:1538-1545
    DOI: 10.1016/j.chaos.2006.04.033
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    1. Fei-Yu Zhang & Wan-Tong Li, 2005. "Global stability of delayed Hopfield neural networks under dynamical thresholds," Discrete Dynamics in Nature and Society, Hindawi, vol. 2005, pages 1-17, January.
    2. Lu, Junwei & Guo, Yiqian & Xu, Shengyuan, 2006. "Global asymptotic stability analysis for cellular neural networks with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 349-353.
    3. Zhang, Qiang & Wei, Xiaopeng & Xu, Jin, 2006. "Stability analysis for cellular neural networks with variable delays," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 331-336.
    4. Mohamad, S. & Gopalsamy, K., 2000. "Dynamics of a class of discrete-time neural networks and their continuous-time counterparts," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 53(1), pages 1-39.
    5. Yang, Haifeng & Chu, Tianguang & Zhang, Cishen, 2006. "Exponential stability of neural networks with variable delays via LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 133-139.
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    Cited by:

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    2. Lan, Heng-you & Cui, Yi-Shun, 2009. "A neural network method for solving a system of linear variational inequalities," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1245-1252.

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