IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i4p436-d503777.html
   My bibliography  Save this article

Dynamics of a Two Prey and One Predator System with Indirect Effect

Author

Listed:
  • Renato Colucci

    (Dipartimento di Ingegneria Industriale e Scienze Matematiche, Università Politecnica delle Marche, Via Brecce Bianche 1, 60131 Ancona, Italy)

  • Érika Diz-Pita

    (Departamento de Estatística, Análise Matemática e Optimización, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain)

  • M. Victoria Otero-Espinar

    (Departamento de Estatística, Análise Matemática e Optimización, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain)

Abstract

We study a population model with two preys and one predator, considering a Holling type II functional response for the interaction between first prey and predator and taking into account indirect effect of predation. We perform the stability analysis of equilibria and study the possibility of Hopf bifurcation. We also include a detailed discussion on the problem of persistence. Several numerical simulations are provided in order to illustrate the theoretical results of the paper.

Suggested Citation

  • Renato Colucci & Érika Diz-Pita & M. Victoria Otero-Espinar, 2021. "Dynamics of a Two Prey and One Predator System with Indirect Effect," Mathematics, MDPI, vol. 9(4), pages 1-22, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:436-:d:503777
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/4/436/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/4/436/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Florencia Carusela, M. & Momo, Fernando R. & Romanelli, Lilia, 2009. "Competition, predation and coexistence in a three trophic system," Ecological Modelling, Elsevier, vol. 220(19), pages 2349-2352.
    2. Renato Colucci & Daniel Nuñez, 2013. "Periodic Orbits for a Three-Dimensional Biological Differential Systems," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, June.
    3. Renato Colucci, 2013. "Coexistence in a One-Predator, Two-Prey System with Indirect Effects," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-13, April.
    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. Sk Golam Mortoja & Prabir Panja & Shyamal Kumar Mondal, 2023. "Stability Analysis of Plankton–Fish Dynamics with Cannibalism Effect and Proportionate Harvesting on Fish," Mathematics, MDPI, vol. 11(13), pages 1-37, July.

    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. Li, Junmin & Huang, Ping & Zhang, Renduo, 2010. "Modeling the refuge effect of submerged macrophytes in ecological dynamics of shallow lakes: A new model of fish functional response," Ecological Modelling, Elsevier, vol. 221(17), pages 2076-2085.

    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:9:y:2021:i:4:p:436-:d:503777. 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: 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.