IDEAS home Printed from https://ideas.repec.org/a/hin/jnddns/9705985.html
   My bibliography  Save this article

Bifurcation Analysis and Chaos Control in a Discrete-Time Predator-Prey System of Leslie Type with Simplified Holling Type IV Functional Response

Author

Listed:
  • S. M. Sohel Rana
  • Umme Kulsum

Abstract

The dynamic behavior of a discrete-time predator-prey system of Leslie type with simplified Holling type IV functional response is examined. We algebraically show that the system undergoes a bifurcation (flip or Neimark-Sacker) in the interior of . Numerical simulations are presented not only to validate analytical results but also to show chaotic behaviors which include bifurcations, phase portraits, period 2, 4, 6, 8, 10, and 20 orbits, invariant closed cycle, and attracting chaotic sets. Furthermore, we compute numerically maximum Lyapunov exponents and fractal dimension to justify the chaotic behaviors of the system. Finally, a strategy of feedback control is applied to stabilize chaos existing in the system.

Suggested Citation

  • S. M. Sohel Rana & Umme Kulsum, 2017. "Bifurcation Analysis and Chaos Control in a Discrete-Time Predator-Prey System of Leslie Type with Simplified Holling Type IV Functional Response," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-11, July.
    • Handle: RePEc:hin:jnddns:9705985
    DOI: 10.1155/2017/9705985
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/DDNS/2017/9705985.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/DDNS/2017/9705985.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2017/9705985?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
    ---><---

    Citations

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


    Cited by:

    1. Rajni, & Ghosh, Bapan, 2022. "Multistability, chaos and mean population density in a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. Blé, Gamaliel & Dela-Rosa, Miguel Angel, 2019. "Neimark–Sacker bifurcation in a tritrophic model with defense in the prey," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 124-139.

    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:hin:jnddns:9705985. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    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.