IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i13p2170-d1693531.html
   My bibliography  Save this article

Bifurcation Analysis of a Predator–Prey Model with Coefficient-Dependent Dual Time Delays

Author

Listed:
  • Xiuling Li

    (College of Applied Mathematics, Jilin University of Finance and Economics, Changchun 130117, China)

  • Siyu Dong

    (College of Applied Mathematics, Jilin University of Finance and Economics, Changchun 130117, China)

Abstract

In this paper, a class of two-delay predator–prey models with coefficient-dependent delay is studied. It examines the combined effect of fear-induced delay and post-predation biomass conversion delay on the stability of predator–prey systems. By analyzing the distribution of roots of the characteristic equation, the stability conditions for the internal equilibrium and the existence criteria for Hopf bifurcations are derived. Utilizing normal form theory and the central manifold theorem, the direction of Hopf bifurcations and the stability of periodic solutions are calculated. Finally, numerical simulations are conducted to verify the theoretical findings. This research reveals that varying delays can destabilize the predator–prey system, reflecting the dynamic complexity of real-world ecosystems more realistically.

Suggested Citation

  • Xiuling Li & Siyu Dong, 2025. "Bifurcation Analysis of a Predator–Prey Model with Coefficient-Dependent Dual Time Delays," Mathematics, MDPI, vol. 13(13), pages 1-23, July.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:13:p:2170-:d:1693531
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/13/2170/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/13/2170/
    Download Restriction: no
    ---><---

    More about this item

    Keywords

    ;
    ;
    ;

    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:gam:jmathe:v:13:y:2025:i:13:p:2170-:d:1693531. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.