IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v34y2007i2p646-653.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077906003481
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2006.03.110?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    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. Lu Pang & Cheng Hu & Juan Yu & Haijun Jiang, 2022. "Fixed-Time Synchronization for Fuzzy-Based Impulsive Complex Networks," Mathematics, MDPI, vol. 10(9), pages 1-16, May.
    7. Mohamad, Sannay, 2008. "Computer simulations of exponentially convergent networks with large impulses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(4), pages 331-344.
    8. Chen, Ling & Zhao, Hongyong, 2008. "Global stability of almost periodic solution of shunting inhibitory cellular neural networks with variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 351-357.
    9. Xia, Yonghui & Huang, Zhenkun & Han, Maoan, 2008. "Exponential p-stability of delayed Cohen–Grossberg-type BAM neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 806-818.
    10. 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.
    11. Zeng, Xu & Li, Chuandong & Huang, Tingwen & He, Xing, 2015. "Stability analysis of complex-valued impulsive systems with time delay," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 75-82.
    12. Wen, Zhen & Sun, Jitao, 2009. "Stability analysis of delayed Cohen–Grossberg BAM neural networks with impulses via nonsmooth analysis," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1829-1837.
    13. 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.
    14. Bing Li & Yongkun Li, 2019. "Existence and Global Exponential Stability of Almost Automorphic Solution for Clifford-Valued High-Order Hopfield Neural Networks with Leakage Delays," Complexity, Hindawi, vol. 2019, pages 1-13, July.
    15. Sun, Jitao & Wang, Qing-Guo & Gao, Hanqiao, 2009. "Periodic solution for nonautonomous cellular neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1423-1427.
    16. Sun, Yeong-Jeu, 2009. "Stability criteria for a class of differential inclusion systems with discrete and distributed time delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2386-2391.
    17. Liu, Hailin & Chen, Guohua, 2007. "Delay-dependent stability for neural networks with time-varying delay," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 171-177.
    18. Liu, Bingwen, 2007. "Almost periodic solutions for Hopfield neural networks with continuously distributed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 73(5), pages 327-335.
    19. 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.
    20. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:34:y:2007:i:2:p:646-653. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.