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Global exponential stability of Cohen-Grossberg neural networks with time-varying delays and impulses

  • Applied Mathematics and Mechanics
  • Published:
Journal of Shanghai University (English Edition)

Abstract

In this paper, the Cohen-Grossberg neural networks with time-varying delays and impulses are considered. New sufficient conditions for the existence and global exponential stability of a unique equilibrium point are established by using the fixed point theorem and Lyapunov functional. An example is given to demonstrate the effectiveness of our results.

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References

  1. Huang Z T, Yang Q G, Luo X. Exponential stability of impulsive neural networks with time-varying delays [J]. Chaos, Solitons and Fractals, 2008, 35(4):770–780.

    Article  MATH  Google Scholar 

  2. Lou X Y, Cui B T. Global asymptotic stability of delay BAM neural networks with impulses [J]. Chaos, Solitons and Fractals, 2006, 29(4): 1023–1031.

    Article  MATH  MathSciNet  Google Scholar 

  3. Liu B W, Huang L H. Global exponential stability of BAM neural networks with recent-history distributed delays and impulses [J]. Neurocomputing, 2006, 69(16):2090–2096.

    Article  Google Scholar 

  4. Xiong W M, Zhou Q Y. Global exponential stability of cellular neural networks with mixed delays and impulses [J]. Chaos, Solitons and Fractals, 2007, 34(3):896–902.

    Article  MATH  MathSciNet  Google Scholar 

  5. Xia Y H, Cao J D, Cheng S S. Global exponential stability of delayed cellular neural networks with impulse [J]. Neurocomputing, 2006, 70(13): 2495–2501.

    Article  Google Scholar 

  6. Gopalsamy K. Stability of artificial neural networks with impulses [J]. Applied Mathematics and Computation, 2004, 154(3): 783–813.

    Article  MATH  MathSciNet  Google Scholar 

  7. Mohamad S. Exponential stability in Hopfield-type neural networks with impulses [J]. Chaos, Solitons and Fractals, 2007, 32(2): 456–467.

    Article  MATH  MathSciNet  Google Scholar 

  8. Bai C Z. Stability analysis of Cohen-Grossberg BAM neural networks with delays and impulse [J]. Chaos, Solitons and Fractals, 2008, 35(2): 263–267.

    Article  MATH  MathSciNet  Google Scholar 

  9. Song Q K, Cao J D. Stability analysis of Cohen-Grossberg neural network with both time-varying and continuously distributed delays [J]. Journal of Computational and Applied Mathematics, 2006, 197(1): 188–203.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  10. Zhang J Y, Suda Y, Komine H. Global exponential stability of Cohen-Grossberg neural networks with variable delays [J]. Physics Letters A, 2005, 338(1): 44–50.

    Article  MATH  ADS  CAS  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Wuhan University of Technology, Wuhan, 430070, P. R. China

    Qing Zhu  (祝 庆), Fang Liang  (梁 芳) & Qing Zhang  (张 青)

Authors
  1. Qing Zhu  (祝 庆)
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  2. Fang Liang  (梁 芳)
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  3. Qing Zhang  (张 青)
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Corresponding author

Correspondence to Qing Zhu  (祝 庆).

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Cite this article

Zhu, Q., Liang, F. & Zhang, Q. Global exponential stability of Cohen-Grossberg neural networks with time-varying delays and impulses. J. Shanghai Univ.(Engl. Ed.) 13, 255–259 (2009). https://doi.org/10.1007/s11741-009-0310-3

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  • DOI: https://doi.org/10.1007/s11741-009-0310-3

Keywords

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