IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i12p1897-d1417807.html
   My bibliography  Save this article

Dynamics for a Ratio-Dependent Prey–Predator Model with Different Free Boundaries

Author

Listed:
  • Lingyu Liu

    (School of Sciences, Civil Aviation Flight University of China, Guanghan 618300, China)

  • Xiaobo Li

    (School of Sciences, Civil Aviation Flight University of China, Guanghan 618300, China)

  • Pengcheng Li

    (School of Sciences, Civil Aviation Flight University of China, Guanghan 618300, China)

Abstract

In this paper, we study the dynamics of the ratio-dependent type prey–predator model with different free boundaries. The two free boundaries, determined by prey and predator, respectively, implying that they may intersect with each other as time evolves, are used to describe the spreading of prey and predator. Our primary focus lies in analyzing the long-term behaviors of both predator and prey. We establish sufficient conditions for the spreading and vanishing of prey and predator. Furthermore, in cases where spread occurs, we offer estimates for the asymptotic spreading speeds of prey and predator, denoted as u and v , respectively, as well as the asymptotic speeds of the free boundaries, denoted by h and g . Our findings reveal that when the predator’s speed is lower than that of the prey, it leads to a reduction in the prey’s asymptotic speed.

Suggested Citation

  • Lingyu Liu & Xiaobo Li & Pengcheng Li, 2024. "Dynamics for a Ratio-Dependent Prey–Predator Model with Different Free Boundaries," Mathematics, MDPI, vol. 12(12), pages 1-18, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:12:p:1897-:d:1417807
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/12/1897/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/12/1897/
    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:12:p:1897-:d:1417807. 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.