IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v41y2009i4p2010-2017.html
   My bibliography  Save this article

Stability and Neimark–Sacker bifurcation of numerical discretization of delay differential equations

Author

Listed:
  • He, Zhimin
  • Lai, Xin
  • Hou, Aiyu

Abstract

A kind of a discrete delay model obtained by Euler method is investigated. Firstly, the linear stability of the model is studied. It is found that there exist Neimark–Sacker bifurcations when the delay passes a sequence of critical values. Then the explicit algorithm for determining the direction and stability of the Neimark–Sacker bifurcations are derived by using the normal form theory and center manifold theorem. Finally, computer simulations are provided to illustrate the analytical results found.

Suggested Citation

  • He, Zhimin & Lai, Xin & Hou, Aiyu, 2009. "Stability and Neimark–Sacker bifurcation of numerical discretization of delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2010-2017.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:4:p:2010-2017
    DOI: 10.1016/j.chaos.2008.08.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077908003639
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2008.08.009?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. 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.
    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. Sami Elmadssia & Karim Saadaoui, 2020. "New Stability Conditions for a Class of Nonlinear Discrete-Time Systems with Time-Varying Delay," Mathematics, MDPI, vol. 8(9), pages 1-19, September.

    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. Zhang, Xue & Zhang, Qing-ling & Zhang, Yue, 2009. "Bifurcations of a class of singular biological economic models," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1309-1318.

    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:41:y:2009:i:4:p:2010-2017. 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.