IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v32y2007i4p1582-1596.html
   My bibliography  Save this article

Global qualitative analysis for a predator–prey system with delay

Author

Listed:
  • Sun, Chengjun
  • Han, Maoan
  • Lin, Yiping
  • Chen, Yuanyuan

Abstract

In this paper, the dynamics of a predator–prey system with a finite delay is considered. The conditions for the global stability and the existence of Hopf bifurcation at the positive equilibrium of the system are obtained. Explicit algorithms for determining the direction of Hopf bifurcations and the stability of bifurcating periodic solutions are derived, using the normal form theory and center manifold argument [Nussbaum RD. Periodic solutions of some nonlinear autonomous functional equations. Ann Mat Pura Appl 1974;10:263–306]. Numerical simulations supporting the theoretical analysis are also given. Global existence of periodic solutions is established by using a global Hopf bifurcation result of Wu [Hassard B, Kazarino D, Wan Y. Theory and applications of Hopf bifurcation. Cambridge: Cambridge University Press; 1981].

Suggested Citation

  • Sun, Chengjun & Han, Maoan & Lin, Yiping & Chen, Yuanyuan, 2007. "Global qualitative analysis for a predator–prey system with delay," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1582-1596.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:4:p:1582-1596
    DOI: 10.1016/j.chaos.2005.11.038
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077905011343
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2005.11.038?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.

    Citations

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


    Cited by:

    1. Elettreby, M.F., 2009. "Two-prey one-predator model," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2018-2027.
    2. Ling, Li & Wang, Weiming, 2009. "Dynamics of a Ivlev-type predator–prey system with constant rate harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2139-2153.
    3. Çelik, Canan & Duman, Oktay, 2009. "Allee effect in a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1956-1962.
    4. Sun, Chengjun & Loreau, Michel, 2009. "Dynamics of a three-species food chain model with adaptive traits," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2812-2819.
    5. Russu, Paolo, 2009. "Hopf bifurcation in a environmental defensive expenditures model with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3147-3159.

    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:32:y:2007:i:4:p:1582-1596. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.