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Existence and attractivity of periodic solutions to non-autonomous Cohen–Grossberg neural networks with time delays

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  • Li, Chun-Hsien
  • Yang, Suh-Yuh

Abstract

In this paper, we investigate the existence and attractivity of periodic solutions to non-autonomous Cohen–Grossberg neural networks with connection time delays for both discrete and distributed cases. By combining the Lyapunov functional method with the contraction mapping principle, we establish several criteria for the existence and global exponential stability of periodic solutions. More interestingly, all the criteria are independent of time delays as well as the delay types, and do not include one another. Several examples with numerical simulations are given to demonstrate the results.

Suggested Citation

  • Li, Chun-Hsien & Yang, Suh-Yuh, 2009. "Existence and attractivity of periodic solutions to non-autonomous Cohen–Grossberg neural networks with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1235-1244.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:3:p:1235-1244
    DOI: 10.1016/j.chaos.2008.05.005
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    References listed on IDEAS

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    1. Li, Chuandong & Liao, Xiaofeng & Zhang, Rong & Prasad, Ashutosh, 2005. "Global robust exponential stability analysis for interval neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 751-757.
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    4. 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.
    5. Li, Yongkun, 2005. "Global exponential stability of BAM neural networks with delays and impulses," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 279-285.
    6. 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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