IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2021i1p17-d707794.html
   My bibliography  Save this article

Spatiotemporal Dynamics in a Predator–Prey Model with Functional Response Increasing in Both Predator and Prey Densities

Author

Listed:
  • Ruizhi Yang

    (Department of Mathematics, Northeast Forestry University, Harbin 150040, China)

  • Qiannan Song

    (Department of Mathematics, Northeast Forestry University, Harbin 150040, China)

  • Yong An

    (Department of Mathematics, Northeast Forestry University, Harbin 150040, China)

Abstract

In this paper, a diffusive predator–prey system with a functional response that increases in both predator and prey densities is considered. By analyzing the characteristic roots of the partial differential equation system, the Turing instability and Hopf bifurcation are studied. In order to consider the dynamics of the model where the Turing bifurcation curve and the Hopf bifurcation curve intersect, we chose the diffusion coefficients d 1 and β as bifurcating parameters. In particular, the normal form of Turing–Hopf bifurcation was calculated so that we could obtain the phase diagram. For parameters in each region of the phase diagram, there are different types of solutions, and their dynamic properties are extremely rich. In this study, we have used some numerical simulations in order to confirm these ideas.

Suggested Citation

  • Ruizhi Yang & Qiannan Song & Yong An, 2021. "Spatiotemporal Dynamics in a Predator–Prey Model with Functional Response Increasing in Both Predator and Prey Densities," Mathematics, MDPI, vol. 10(1), pages 1-15, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2021:i:1:p:17-:d:707794
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/1/17/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/1/17/
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Shivam, & Singh, Kuldeep & Kumar, Mukesh & Dubey, Ramu & Singh, Teekam, 2022. "Untangling role of cooperative hunting among predators and herd behavior in prey with a dynamical systems approach," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. Abbasi, Muhammad Aqib & Samreen, Maria, 2024. "Analyzing multi-parameter bifurcation on a prey–predator model with the Allee effect and fear effect," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).

    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:10:y:2021:i:1:p:17-:d:707794. 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.