IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2012y2012i1n909385.html

Bifurcation of a Cohen‐Grossberg Neural Network with Discrete Delays

Author

Listed:
  • Qiming Liu
  • Wang Zheng

Abstract

A simple Cohen‐Grossberg neural network with discrete delays is investigated in this paper. The existence of local Hopf bifurcations is first considered by choosing the appropriate bifurcation parameter, and then explicit formulas are given to determine the direction of Hopf bifurcation and stability of the periodic solutions. Moreover, a set of sufficient conditions are given to guarantee the global Hopf bifurcation. Numerical simulations are given to illustrate the obtained results.

Suggested Citation

  • Qiming Liu & Wang Zheng, 2012. "Bifurcation of a Cohen‐Grossberg Neural Network with Discrete Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:909385
    DOI: 10.1155/2012/909385
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2012/909385
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2012/909385?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
    ---><---

    References listed on IDEAS

    as
    1. Yang, Yu & Ye, Jin, 2009. "Stability and bifurcation in a simplified five-neuron BAM neural network with delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2357-2363.
    2. Huang, Zhenkun & Xia, Yonghui, 2009. "Exponential periodic attractor of impulsive BAM networks with finite distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 373-384.
    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. Qiming Liu & Sumin Yang, 2014. "Stability and Hopf Bifurcation of an n‐Neuron Cohen‐Grossberg Neural Network with Time Delays," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).

    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. Qiming Liu & Sumin Yang, 2014. "Stability and Hopf Bifurcation of an n‐Neuron Cohen‐Grossberg Neural Network with Time Delays," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    2. Ye, Zhiyong & Zhang, He & Zhang, Hongyu & Zhang, Hua & Lu, Guichen, 2015. "Mean square stabilization and mean square exponential stabilization of stochastic BAM neural networks with Markovian jumping parameters," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 156-165.
    3. Liang, Wei & Zhang, Yongjun & Zhang, Xuanxuan, 2024. "Chaotic behavior of two discrete-time coupled neurons with two delays," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    4. Huang, Zhenkun & Wang, Xinghua & Xia, Yonghui, 2009. "A topological approach to the existence of solutions for nonlinear differential equations with piecewise constant argument," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1121-1131.
    5. Qiming Liu & Rui Xu, 2012. "Periodic Solutions of a Cohen‐Grossberg‐Type BAM Neural Networks with Distributed Delays and Impulses," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    6. Wang, Yangling & Cao, Jinde & Xiao, Min & Huang, Chengdai & Zhao, Lingzhi, 2026. "A fractional-order four-layer neural network involving mixed time delays: Hopf bifurcation analysis," Chaos, Solitons & Fractals, Elsevier, vol. 203(C).
    7. Tetie Pan & Bao Shi & Jian Yuan, 2012. "Global Stability of Almost Periodic Solution of a Class of Neutral‐Type BAM Neural Networks," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    8. Wang, Yangling & Cao, Jinde & Huang, Chengdai, 2022. "Exploration of bifurcation for a fractional-order BAM neural network with n+2 neurons and mixed time delays," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

    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:wly:jnlaaa:v:2012:y:2012:i:1:n:909385. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    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.