IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v236y2025icp183-199.html
   My bibliography  Save this article

Impact of cross-diffusion and Allee effect on modified Leslie–Gower model

Author

Listed:
  • Menon, Sidharth
  • Kumari, Sangeeta

Abstract

A modified Leslie–Gower model with cross-diffusion and Allee effect is studied. First temporal dynamics of the system is analyzed and the existence of equilibrium points and their corresponding stability analysis are performed. Variation in the Allee effect parameter results in saddle node and Hopf bifurcations. Further, the spatio-temporal model is analyzed and observed that as cross-diffusion gradually increases, prey and predator disperse over the region. Turing instability conditions are derived for cross-diffusion and stability analysis of the amplitude equations is computed to identify the type of the Turing pattern. Analytical conclusions are validated through numerical simulations. As the Allee effect increases, it affects the spatial and temporal dynamics of the prey population. Turing pattern changes from spots to stripes, indicating a large dispersion and a variety of predator interactions, which reduces confinement to secure small areas. In the absence of cross-diffusion, there will be a positive correlation between prey and predator populations. In contrast, when cross-diffusion is present, a negative correlation between prey and predator populations arises.

Suggested Citation

  • Menon, Sidharth & Kumari, Sangeeta, 2025. "Impact of cross-diffusion and Allee effect on modified Leslie–Gower model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 236(C), pages 183-199.
    • Handle: RePEc:eee:matcom:v:236:y:2025:i:c:p:183-199
    DOI: 10.1016/j.matcom.2025.03.031
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475425001168
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2025.03.031?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:236:y:2025:i:c:p:183-199. 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.