IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v39y2009i1p83-91.html
   My bibliography  Save this article

Bifurcation analysis for a discrete-time Hopfield neural network of two neurons with two delays and self-connections

Author

Listed:
  • Kaslik, E.
  • Balint, St.

Abstract

In this paper, a bifurcation analysis is undertaken for a discrete-time Hopfield neural network of two neurons with two different delays and self-connections. Conditions ensuring the asymptotic stability of the null solution are found, with respect to two characteristic parameters of the system. It is shown that for certain values of these parameters, Fold or Neimark-Sacker bifurcations occur, but Flip and codimension 2 (Fold–Neimark-Sacker, double Neimark-Sacker, resonance 1:1 and Flip–Neimark-Sacker) bifurcations may also be present. The direction and the stability of the Neimark-Sacker bifurcations are investigated by applying the center manifold theorem and the normal form theory.

Suggested Citation

  • Kaslik, E. & Balint, St., 2009. "Bifurcation analysis for a discrete-time Hopfield neural network of two neurons with two delays and self-connections," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 83-91.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:1:p:83-91
    DOI: 10.1016/j.chaos.2007.01.126
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077907002603
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2007.01.126?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. 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.
    2. Zhang, Chunrui & Zheng, Baodong, 2005. "Hopf bifurcation in numerical approximation of a n-dimension neural network model with multi-delays," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 129-146.
    3. Zhang, Chunrui & Zheng, Baodong, 2007. "Stability and bifurcation of a two-dimension discrete neural network model with multi-delays," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1232-1242.
    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. Wan, Li & Zhou, Qinghua & Liu, Jie, 2017. "Delay-dependent attractor analysis of Hopfield neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 68-72.

    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. 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. Yang, Xiaofan & Yang, Maobin & Liu, Huaiyi & Liao, Xiaofeng, 2008. "Bautin bifurcation in a class of two-neuron networks with resonant bilinear terms," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 575-589.
    3. 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.
    4. Li, Fengjun & Xu, Zongben, 2008. "The estimation of simultaneous approximation order for neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 572-580.
    5. Yang, Degang & Hu, Chunyan & Chen, Yong & Wei, Pengcheng & Yang, Huaqian, 2009. "New delay-dependent global asymptotic stability criteria of delayed BAM neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 854-864.
    6. Wang, Hongbin & Jiang, Weihua, 2006. "Multiple stabilities analysis in a magnetic bearing system with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 789-799.
    7. Binhao Hong & Chunrui Zhang, 2023. "Neimark–Sacker Bifurcation of a Discrete-Time Predator–Prey Model with Prey Refuge Effect," Mathematics, MDPI, vol. 11(6), pages 1-13, March.
    8. Zhang, Chunrui & Zheng, Baodong, 2007. "Stability and bifurcation of a two-dimension discrete neural network model with multi-delays," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1232-1242.
    9. Zheng, Baodong & Zhang, Yang & Zhang, Chunrui, 2008. "Stability and bifurcation of a discrete BAM neural network model with delays," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 612-616.
    10. Zhang, Chunrui & Zu, Yuangang & Zheng, Baodong, 2006. "Stability and bifurcation of a discrete red blood cell survival model," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 386-394.
    11. Gan, Qintao & Xu, Rui & Hu, Wenhua & Yang, Pinghua, 2009. "Bifurcation analysis for a tri-neuron discrete-time BAM neural network with delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2502-2511.

    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:39:y:2009:i:1:p:83-91. 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.