IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i23p3748-d1531798.html
   My bibliography  Save this article

Bifurcation Branch in a Spatial Heterogeneous Predator–Prey Model with a Nonlinear Growth Rate for the Predator

Author

Listed:
  • Lei Kong

    (College of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China)

Abstract

A strongly coupled predator–prey model in a spatially heterogeneous environment with a Holling type-II functional response and a nonlinear growth rate for the predator is considered. Using bifurcation theory and the Lyapunov–Schmidt reduction, we derived a bounded smooth curve formed by the positive solutions and obtained the structure of the bifurcation branches. We also proved that the bounded curve is monotone S -shaped or fish-hook-shaped (⊂-shaped), as the values of the parameters of the model vary; in the latter case, the model has multiple positive steady-state solutions caused by the spatial heterogeneity of the environment.

Suggested Citation

  • Lei Kong, 2024. "Bifurcation Branch in a Spatial Heterogeneous Predator–Prey Model with a Nonlinear Growth Rate for the Predator," Mathematics, MDPI, vol. 12(23), pages 1-18, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3748-:d:1531798
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/23/3748/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/23/3748/
    Download Restriction: no
    ---><---

    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:12:y:2024:i:23:p:3748-:d:1531798. 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.