IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v94y2013icp33-54.html
   My bibliography  Save this article

Global qualitative analysis of a predator–prey system with Allee effect on the prey species

Author

Listed:
  • Zu, Jian

Abstract

In this paper, the Allee effect is incorporated into a predator–prey model with linear functional response. Compared with the predator–prey model without the Allee effect, it is found that the Allee effect of the prey species increases the extinction risk of both the prey and predator. If the Allee effect of the prey species is strong and the mortality of the predator species is relatively low, then the prey and predator cannot coexist after the predator invasion. Moreover, it is shown that the model with Allee effect undergoes the heteroclinic loop bifurcation and subcritical and supercritical Hopf bifurcations. With the brokenness of the heteroclinic loop, a stable or unstable limit cycle will appear. The Allee effect of the prey species can lead to unstable or stable periodic fluctuations. It is also found that the positive equilibrium of the model could change from stable to unstable, and then disappear when the strength of Allee effect increases continuously from zero.

Suggested Citation

  • Zu, Jian, 2013. "Global qualitative analysis of a predator–prey system with Allee effect on the prey species," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 33-54.
  • Handle: RePEc:eee:matcom:v:94:y:2013:i:c:p:33-54
    DOI: 10.1016/j.matcom.2013.05.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475413001523
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2013.05.009?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. Tian, Yuan & Sun, Kaibiao & Chen, Lansun, 2011. "Modelling and qualitative analysis of a predator–prey system with state-dependent impulsive effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(2), pages 318-331.
    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. Li, Xiaoshuang & Pang, Danfeng & Wallhead, Philip & Bellerby, Richard Garth James, 2023. "Dynamics of an aquatic diffusive predator–prey model with double Allee effect and pH-dependent capture rate," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    2. Kumar, Udai & Mandal, Partha Sarathi, 2022. "Role of Allee effect on prey–predator model with component Allee effect for predator reproduction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 623-665.

    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. Tian, Yuan & Li, Chunxue & Liu, Jing, 2023. "Complex dynamics and optimal harvesting strategy of competitive harvesting models with interval-valued imprecise parameters," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    2. Jana, Soovoojeet & Chakraborty, Milon & Chakraborty, Kunal & Kar, T.K., 2012. "Global stability and bifurcation of time delayed prey–predator system incorporating prey refuge," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 85(C), pages 57-77.
    3. Yangyang Su & Tongqian Zhang, 2022. "Global Dynamics of a Predator–Prey Model with Fear Effect and Impulsive State Feedback Control," Mathematics, MDPI, vol. 10(8), pages 1-23, April.
    4. Sun, Kaibiao & Zhang, Tonghua & Tian, Yuan, 2017. "Dynamics analysis and control optimization of a pest management predator–prey model with an integrated control strategy," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 253-271.
    5. Li, Wenjie & Huang, Lihong & Guo, Zhenyuan & Ji, Jinchen, 2020. "Global dynamic behavior of a plant disease model with ratio dependent impulsive control strategy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 120-139.

    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:matcom:v:94:y:2013:i:c:p:33-54. 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/mathematics-and-computers-in-simulation/ .

    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.