IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v516y2019icp402-411.html
   My bibliography  Save this article

Detection and computation of high codimension bifurcations in diffuse predator–prey systems

Author

Listed:
  • Diouf, A.
  • Mokrani, H.
  • Ngom, D.
  • Haque, M.
  • Camara, B.I.

Abstract

In this paper, we consider reaction–diffusion model with modified Leslie–Gower and Holling-type II functional response and by varying simultaneously three model parameters, our model exhibits different types of complex dynamics. This allowed us to delimit several bifurcation surfaces with higher codimension corresponding to: Turing, Turing-Transcritical, Turing–Bogdanov–Taken, Turing–Hopf–Andronov, Turing-Saddle–node. Moreover by varying at least three bifurcation parameters, we show that small variations in the ratio of the diffusion coefficients can significantly alter bifurcation structure. Finally, the paper ends with the emergence of spatio-temporal patterns via numerical simulations. These simultaneous parameter variations leaded to spatio-temporal local and global bifurcations which are always catastrophic. Our results give new insights about how simultaneous changes in environmental and life history parameters drive different distribution dynamics of predator–prey populations. This only underscores the importance of including global bifurcations in the analysis of food chain models. Such results can be used to improve ecological decision-making on species conservation.

Suggested Citation

  • Diouf, A. & Mokrani, H. & Ngom, D. & Haque, M. & Camara, B.I., 2019. "Detection and computation of high codimension bifurcations in diffuse predator–prey systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 402-411.
    • Handle: RePEc:eee:phsmap:v:516:y:2019:i:c:p:402-411
    DOI: 10.1016/j.physa.2018.10.027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437118313657
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2018.10.027?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.

    References listed on IDEAS

    as
    1. Shengbin Yu, 2012. "Global Asymptotic Stability of a Predator-Prey Model with Modified Leslie-Gower and Holling-Type II Schemes," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-8, July.
    2. Kiran D’Souza & Bogdan I Epureanu & Mercedes Pascual, 2015. "Forecasting Bifurcations from Large Perturbation Recoveries in Feedback Ecosystems," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-19, September.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Chen, Mengxin & Wu, Ranchao & Chen, Liping, 2020. "Spatiotemporal patterns induced by Turing and Turing-Hopf bifurcations in a predator-prey system," Applied Mathematics and Computation, Elsevier, vol. 380(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Manfred Füllsack & Simon Plakolb & Georg Jäger, 2021. "Predicting regime shifts in social systems modelled with agent-based methods," Journal of Computational Social Science, Springer, vol. 4(1), pages 163-185, May.
    2. Manfred Füllsack & Daniel Reisinger, 2021. "Transition prediction in the Ising-model," PLOS ONE, Public Library of Science, vol. 16(11), pages 1-14, November.

    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:phsmap:v:516:y:2019:i:c:p:402-411. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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/physica-a-statistical-mechpplications/ .

    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.