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Harmless delays for global asymptotic stability of Cohen–Grossberg neural networks

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  • Tu, Fenghua
  • Liao, Xiaofeng

Abstract

In this paper, the Cohen–Grossberg neural network models with time delays are considered without assuming the symmetry of connection matrix as well as the monotonicity and differentiability of the activation functions and the self-signal functions. By constructing a novel Lyapunov functional, sufficient criteria for the existence of a unique equilibrium and global asymptotic stability of the network are derived. These criteria are all independent of the magnitudes of the delays, and so the delays under these conditions are harmless. Our results are less conservative and restrictive than previously known results and can be easily verified. In the meantime, our approach does not need to fulfill the rigorous conditions of the amplification functions. It is believed that our results are significant and useful for the design and applications of the Cohen–Grossberg model.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:3:p:927-933
    DOI: 10.1016/j.chaos.2005.01.045
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    Cited by:

    1. Sun, Yeong-Jeu, 2007. "Stability criterion for a class of descriptor systems with discrete and distributed time delays," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 986-993.
    2. 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.
    3. Park, Ju H., 2007. "An analysis of global robust stability of uncertain cellular neural networks with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 800-807.
    4. Sun, Yeong-Jeu, 2007. "Duality between observation and output feedback for linear systems with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 879-884.
    5. 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.
    6. 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.
    7. Xiong, Wenjun & Ma, Deyi & Liang, Jinling, 2009. "Robust convergence of Cohen–Grossberg neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1176-1184.
    8. 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.
    9. Zhao, Weirui & Tan, Yong, 2007. "Harmless delays for global exponential stability of Cohen–Grossberg neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 74(1), pages 47-57.
    10. Huang, Tingwen & Li, Chuandong & Chen, Goong, 2007. "Stability of Cohen–Grossberg neural networks with unbounded distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 992-996.

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