IDEAS home Printed from https://ideas.repec.org/a/hin/jnddns/4555469.html
   My bibliography  Save this article

Dynamical Complexities of a Discrete Ivlev-Type Predator-Prey System

Author

Listed:
  • Sarker Md. Sohel Rana
  • A. E. Matouk

Abstract

In this study, we examine a discrete predator-prey system from the following two perspectives: (i) the functional response is of the Ivlev type and (ii) the prey growth rate is of the Gompertz type. We define the stability requirement for feasible fixed points. We demonstrate algebraically that if the bifurcation (control) parameter rises over its threshold value, the system encounters flip and Neimark–Sacker (NS) bifurcations in the vicinity of the interior fixed point. We explicitly establish the existence requirements and direction of bifurcations via the center manifold theory. Analytical findings are validated by numerical simulations, which are used to highlight the occurrence of instability and chaotic dynamics in the system. In order to regulate the chaotic trajectories that exist in the system, we adopt a feedback control approach.

Suggested Citation

  • Sarker Md. Sohel Rana & A. E. Matouk, 2023. "Dynamical Complexities of a Discrete Ivlev-Type Predator-Prey System," Discrete Dynamics in Nature and Society, Hindawi, vol. 2023, pages 1-14, February.
    • Handle: RePEc:hin:jnddns:4555469
    DOI: 10.1155/2023/4555469
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/ddns/2023/4555469.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/ddns/2023/4555469.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2023/4555469?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
    ---><---

    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:4555469. 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.