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A further analysis on harmless delays in Cohen–Grossberg neural networks

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  • Li, Chun-Hsien
  • Yang, Suh-Yuh

Abstract

Without assuming the monotonicity and differentiability of activation functions and the symmetry of interconnections, Wang and Zou [Wang L, Zou X. Harmless delays in Cohen–Grossberg neural networks, Physica D 2002;170:162–73] established three sufficient conditions for the global asymptotic stability of a unique equilibrium of the Cohen–Grossberg neural network with multiple discrete time delays. These criteria are all independent of the magnitudes of the delays, and so the time delays under these conditions are harmless. More interestingly, their numerical results indicate that the first two of these criteria actually ensure the global exponential stability of the unique equilibrium. In this paper, we will provide rigorous proofs of these numerical observations. Some further numerical simulations are given to illustrate the theoretical results.

Suggested Citation

  • Li, Chun-Hsien & Yang, Suh-Yuh, 2007. "A further analysis on harmless delays in Cohen–Grossberg neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 646-653.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:2:p:646-653
    DOI: 10.1016/j.chaos.2006.03.110
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    References listed on IDEAS

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    1. Liu, Jiang, 2005. "Global exponential stability of Cohen–Grossberg neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 935-945.
    2. Tu, Fenghua & Liao, Xiaofeng, 2005. "Harmless delays for global asymptotic stability of Cohen–Grossberg neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 927-933.
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    Cited by:

    1. Ping, Zhao Wu & Lu, Jun Guo, 2009. "Global exponential stability of impulsive Cohen–Grossberg neural networks with continuously distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 164-174.
    2. Li, Chun-Hsien & Yang, Suh-Yuh, 2009. "Global attractivity in delayed Cohen–Grossberg neural network models," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1975-1987.

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