IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v157y2022ics096007792200131x.html
   My bibliography  Save this article

Biological control in a simple ecological model via subcritical Hopf and Bogdanov-Takens bifurcations

Author

Listed:
  • Chan-López, E.
  • Castellanos, Víctor

Abstract

Parasitoids are ubiquitous in nature and they play a fundamental role in the equilibrium of ecosystems. Their interactions with other species are particularly crucial for agricultural activities, since they act as a biological control of invasive hosts. In this paper we study Hopf, generalized Hopf and nondegenerate Bogdanov-Takens bifurcations in a simple model which describes the biological control of invasive species through predation by generalist parasitoids. We assume logistic growth for the generalist parasitoid in the absence of host species, and their interaction is described by a Holling type II functional response. We determine a geometric condition which characterizes local bifurcations associated with the appearance of periodic orbits. Further, we find conditions on the parameters which yield to the extinction of the host species, independently of the initial conditions and the charge capacity of the generalist parasitoid. Our results are supported by numerical examples.

Suggested Citation

  • Chan-López, E. & Castellanos, Víctor, 2022. "Biological control in a simple ecological model via subcritical Hopf and Bogdanov-Takens bifurcations," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s096007792200131x
    DOI: 10.1016/j.chaos.2022.111921
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007792200131X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.111921?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:chsofr:v:157:y:2022:i:c:s096007792200131x. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.