IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v79y2009i5p1527-1543.html
   My bibliography  Save this article

New criteria for globally exponential stability of delayed Cohen–Grossberg neural network

Author

Listed:
  • Chen, Shengshuang
  • Zhao, Weirui
  • Xu, Yong

Abstract

This paper is concerned with analysis problem for the global exponential stability of the Cohen–Grossberg neural networks with discrete delays and with distributed delays. We first prove the existence and uniqueness of the equilibrium point under mild conditions, assuming neither differentiability nor strict monotonicity for the activation function. Then, we employ Lyapunov functions to establish some sufficient conditions ensuring global exponential stability of equilibria for the Cohen–Grossberg neural networks with discrete delays and with distributed delays. Our results are not only presented in terms of system parameters and can be easily verified and also less restrictive than previously known criteria. A comparison between our results and the previous results admits that our results establish a new set of stability criteria for delayed neural networks.

Suggested Citation

  • Chen, Shengshuang & Zhao, Weirui & Xu, Yong, 2009. "New criteria for globally exponential stability of delayed Cohen–Grossberg neural network," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1527-1543.
    • Handle: RePEc:eee:matcom:v:79:y:2009:i:5:p:1527-1543
    DOI: 10.1016/j.matcom.2008.07.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475408002395
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2008.07.002?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. Mohamad, S. & Gopalsamy, K., 2000. "Dynamics of a class of discrete-time neural networks and their continuous-time counterparts," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 53(1), pages 1-39.
    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. Zhang, Zhongjie & Yu, Tingting & Zhang, Xian, 2022. "Algebra criteria for global exponential stability of multiple time-varying delay Cohen–Grossberg neural networks," Applied Mathematics and Computation, Elsevier, vol. 435(C).

    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. 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.
    2. Kaslik, E. & Balint, St., 2007. "Bifurcation analysis for a two-dimensional delayed discrete-time Hopfield neural network," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1245-1253.
    3. Yang, Xiaofan & Liao, Xiaofeng & Megson, Graham M. & Evans, David J., 2005. "Global exponential periodicity of a class of neural networks with recent-history distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 441-447.
    4. Kumar, Amit & Peeta, Srinivas, 2015. "A day-to-day dynamical model for the evolution of path flows under disequilibrium of traffic networks with fixed demand," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 235-256.
    5. Gui, Zhanji & Ge, Weigao, 2007. "Periodic solutions of nonautonomous cellular neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1760-1771.
    6. Zhang, Qiang & Xu, Xiaopeng Wei Jin, 2007. "Delay-dependent global stability results for delayed Hopfield neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 662-668.
    7. Huo, Hai-Feng & Li, Wan-Tong, 2009. "Dynamics of continuous-time bidirectional associative memory neural networks with impulses and their discrete counterparts," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2218-2229.
    8. Jiang, Haijun & Teng, Zhidong, 2006. "Boundedness and global stability for nonautonomous recurrent neural networks with distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 83-93.
    9. Chu, Tianguang & Yang, Haifeng, 2007. "A note on exponential convergence of neural networks with unbounded distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1538-1545.
    10. Gu, Yajuan & Wang, Hu & Yu, Yongguang, 2020. "Synchronization for fractional-order discrete-time neural networks with time delays," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    11. Huang, Zhenkun & Mohamad, Sannay & Gao, Feng, 2014. "Multi-almost periodicity in semi-discretizations of a general class of neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 101(C), pages 43-60.

    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:matcom:v:79:y:2009:i:5:p:1527-1543. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.