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Global attractivity in delayed Cohen–Grossberg neural network models

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  • Li, Chun-Hsien
  • Yang, Suh-Yuh

Abstract

In this paper, we investigate the global attractivity of Cohen–Grossberg neural network models with connection time delays for both discrete and distributed cases via the Lyapunov functional method. Without assuming the monotonicity and differentiability of activation functions and the symmetry of connection matrix, we establish three new sufficient conditions for the global exponential stability of a unique equilibrium for the delayed Cohen–Grossberg neural network no matter whether the connection time delay is of discrete type or distributed type. In particular, all the three new criteria are independent of time delays and do not include one another. To demonstrate the differences and features of the new stability criteria, several examples are discussed to compare the present results with the existing ones.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:4:p:1975-1987
    DOI: 10.1016/j.chaos.2007.06.064
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    References listed on IDEAS

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    1. Bai, Chuanzhi, 2008. "Stability analysis of Cohen–Grossberg BAM neural networks with delays and impulses," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 263-267.
    2. Xiong, WeiLi & Xu, BaoGuo, 2008. "Some criteria for robust stability of Cohen–Grossberg neural networks with delays," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1357-1365.
    3. 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.
    4. 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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