IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v36y2008i5p1366-1376.html
   My bibliography  Save this article

Chaos and Hopf bifurcation of a hybrid ratio-dependent three species food chain

Author

Listed:
  • Wang, Fengyan
  • Pang, Guoping

Abstract

In this paper, we propose and study a model of a hybrid ratio-dependent three species food chain, which is constituted by a hybrid type subsystem of prey and middle-predator and a middle-top predators’ subsystem with Holling type-II functional response. We investigate the persistence and Hopf bifurcation of the system. Computer simulations are carried out to explain the mathematical conclusions. The chaotic attractor is obtained for suitable choice of parametric values.

Suggested Citation

  • Wang, Fengyan & Pang, Guoping, 2008. "Chaos and Hopf bifurcation of a hybrid ratio-dependent three species food chain," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1366-1376.
    • Handle: RePEc:eee:chsofr:v:36:y:2008:i:5:p:1366-1376
    DOI: 10.1016/j.chaos.2006.09.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077906008125
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2006.09.005?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. Wang, Fengyan & Zhang, Shuwen & Chen, Lansun & Sun, Lihua, 2006. "Bifurcation and complexity of Monod type predator–prey system in a pulsed chemostat," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 447-458.
    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. Shang, Zuchong & Qiao, Yuanhua, 2024. "Complex dynamics of a four-species food web model with nonlinear top predator harvesting and fear effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 458-484.
    2. Jiang, Yongxin & Yang, Jianping, 2009. "Complex dynamics in a food chain with slow and fast processes," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3160-3168.

    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. Wang, Weiming & Wang, Xiaoqin & Lin, Yezhi, 2008. "Complicated dynamics of a predator–prey system with Watt-type functional response and impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1427-1441.
    2. Pang, Guoping & Wang, Fengyan & Chen, Lansun, 2009. "Extinction and permanence in delayed stage-structure predator–prey system with impulsive effects," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2216-2224.
    3. Wang, Xiaoqin & Wang, Weiming & Lin, Yezhi & Lin, Xiaolin, 2009. "The dynamical complexity of an impulsive Watt-type prey–predator system," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 731-744.
    4. Wang, Fengyan & Pang, Guoping & Lu, Zhengyi, 2009. "Analysis of a Beddington–DeAngelis food chain chemostat with periodically varying dilution rate," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1609-1615.
    5. Jiang, Zhichao & Wei, Junjie, 2008. "Stability and bifurcation analysis in a delayed SIR model," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 609-619.
    6. Gan, Qintao & Xu, Rui & Yang, Pinghua, 2009. "Bifurcation and chaos in a ratio-dependent predator–prey system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1883-1895.
    7. Pang, Guoping & Wang, Fengyan & Chen, Lansun, 2008. "Analysis of a Monod–Haldene type food chain chemostat with periodically varying substrate," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 731-742.
    8. Wang, Fengyan & Zeng, Guangzhao, 2007. "Chaos in a Lotka–Volterra predator–prey system with periodically impulsive ratio-harvesting the prey and time delays," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1499-1512.
    9. Wang, Xiaoqin & Wang, Weiming & Lin, Xiaolin, 2008. "Chaotic behavior of a Watt-type predator–prey system with impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 706-718.
    10. Wang, Xiaoqin & Wang, Weiming & Lin, Xiaolin, 2009. "Dynamics of a two-prey one-predator system with Watt-type functional response and impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2392-2404.
    11. Toth, Damon J.A., 2008. "Strong resonance and chaos in a single-species chemostat model with periodic pulsing of resource," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 55-69.

    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:36:y:2008:i:5:p:1366-1376. 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.