IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v23y2005i4p1475-1489.html
   My bibliography  Save this article

Stability and bifurcation of a simple food chain in a chemostat with removal rates

Author

Listed:
  • El-Sheikh, M.M.A.
  • Mahrouf, S.A.A.

Abstract

In this paper we consider a model describing predator–prey interactions in a chemostat that incorporates genreal response functions and distinct removal rates. In this case, the conservation law fails. To overcome this problem, we use Liapunov functions in the study of the global stability of equlibria. Mathematical analysis of the model equations with regard to invariance of non-negativity, boundedness of solutions, dissipativity and persistence are studied. Hopf bifurcation theory is applied.

Suggested Citation

  • El-Sheikh, M.M.A. & Mahrouf, S.A.A., 2005. "Stability and bifurcation of a simple food chain in a chemostat with removal rates," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1475-1489.
    • Handle: RePEc:eee:chsofr:v:23:y:2005:i:4:p:1475-1489
    DOI: 10.1016/j.chaos.2004.06.079
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077904004254
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2004.06.079?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. Xiang, Zhongyi & Song, Xinyu, 2007. "A model of competition between plasmid-bearing and plasmid-free organisms in a chemostat with periodic input," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1419-1428.
    2. Xu, Rui & Ma, Zhien, 2008. "Stability and Hopf bifurcation in a ratio-dependent predator–prey system with stage structure," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 669-684.
    3. Gwaltney, C. Ryan & Luo, WenTao & Stadtherr, Mark A., 2007. "Computation of equilibrium states and bifurcations using interval analysis: Application to food chain models," Ecological Modelling, Elsevier, vol. 203(3), pages 495-510.
    4. Jiao, Jianjun & Yang, Xiaosong & Chen, Lansun & Cai, Shaohong, 2009. "Effect of delayed response in growth on the dynamics of a chemostat model with impulsive input," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2280-2287.
    5. Zhang, Yujuan & Xiu, Zhilong & Chen, Lansun, 2005. "Chaos in a food chain chemostat with pulsed input and washout," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 159-166.

    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:23:y:2005:i:4:p:1475-1489. 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.