IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v408y2021ics0096300321004574.html
   My bibliography  Save this article

Global dynamics of a Beddington–DeAngelis amensalism system with weak Allee effect on the first species

Author

Listed:
  • Luo, Demou
  • Wang, Qiru

Abstract

In this paper, we study the global dynamics for a Beddington–DeAngelis amensalism model with strong Allee effect on the second species. We treat the maximum value (which per capita reduction rate of the first species) δ as a bifurcation parameter to analyze various possible bifurcations of the system. We analyze the existence and stability of boundary equilibria, positive equilibria and infinite singularity. Additionally, we show that the system under study can not possess global asymptotic stability by the existence of two stable equilibria in the first quadrant. By the existence of all possible equilibria and their stability, saddle connection and the non-existence of close orbits, we derive two conditions for two transcritical bifurcations. Meanwhile, we offer the global phase portraits of this system. Furthermore, we comprise weak Allee effect on the harmed species and offer a new analysis of equilibria and dynamical discussion of the system. Finally, some numerical simulations are offered to support our main theoretical results.

Suggested Citation

  • Luo, Demou & Wang, Qiru, 2021. "Global dynamics of a Beddington–DeAngelis amensalism system with weak Allee effect on the first species," Applied Mathematics and Computation, Elsevier, vol. 408(C).
    • Handle: RePEc:eee:apmaco:v:408:y:2021:i:c:s0096300321004574
    DOI: 10.1016/j.amc.2021.126368
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300321004574
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2021.126368?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.

    Citations

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


    Cited by:

    1. Zhang, Limin & Wang, Tao, 2023. "Qualitative properties, bifurcations and chaos of a discrete predator–prey system with weak Allee effect on the predator," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

    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:apmaco:v:408:y:2021:i:c:s0096300321004574. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.