IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v229y2025icp32-49.html
   My bibliography  Save this article

Dynamics of a Leslie–Gower type predator–prey system with herd behavior and constant harvesting in prey

Author

Listed:
  • Yao, Yong

Abstract

In this paper, the dynamics of a Leslie–Gower type predator–prey system with herd behavior and constant harvesting in prey are investigated. Earlier work has shown that the herd behavior in prey merely induces a supercritical Hopf bifurcation in the classic Leslie–Gower predator–prey system in the absence of harvesting. However, the work in this paper shows that the presence of herd behavior and constant harvesting in prey can give rise to numerous kinds of bifurcation at the non-hyperbolic equilibria in the classic Leslie–Gower predator–prey system such as two saddle–node bifurcations and one Bogdanov–Takens bifurcation of codimension two at the degenerate equilibria and one degenerate Hopf bifurcation of codimension three at the weak focus. Some numerical simulations are also provided to verify the theoretical results and evaluate their biological implications such as the changes of phase diagram near the degenerate equilibrium due to the Bogdanov–Takens bifurcation and the coexistence of multiple limit cycles arising from the degenerate Hopf bifurcation. Hence, the research results reveal that the herd behavior and constant harvesting in prey have a strong influence on the dynamics and also contribute to promoting the ecological diversity and maintaining the long-term economic benefits.

Suggested Citation

  • Yao, Yong, 2025. "Dynamics of a Leslie–Gower type predator–prey system with herd behavior and constant harvesting in prey," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 229(C), pages 32-49.
  • Handle: RePEc:eee:matcom:v:229:y:2025:i:c:p:32-49
    DOI: 10.1016/j.matcom.2024.09.026
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475424003811
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2024.09.026?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.

    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:matcom:v:229:y:2025:i:c:p:32-49. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.