IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i8p1281-d393949.html
   My bibliography  Save this article

Dynamic Behaviors of a Single Species Stage Structure Model with Michaelis–Menten-TypeJuvenile Population Harvesting

Author

Listed:
  • Xiangqin Yu

    (College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, China)

  • Zhenliang Zhu

    (College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, China)

  • Fengde Chen

    (College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, China)

Abstract

A single species stage structure model with Michaelis–Menten-type juvenile population harvesting is proposed and investigated. The existence and local stability of the model equilibria are studied. It shows that for the model, two cases of bistability may exist. Some conditions for the global asymptotic stability of the boundary equilibrium are derived by constructing some suitable Lyapunov functions. After that, based on the Bendixson–Dulac discriminant, we obtain the sufficient conditions for the global asymptotic stability of the internal equilibrium. Our study shows that nonlinear harvesting can make the dynamics of the system more complex than linear harvesting; for example, the system may admit the bistable stability property. Numeric simulations support our theoretical results.

Suggested Citation

  • Xiangqin Yu & Zhenliang Zhu & Fengde Chen, 2020. "Dynamic Behaviors of a Single Species Stage Structure Model with Michaelis–Menten-TypeJuvenile Population Harvesting," Mathematics, MDPI, vol. 8(8), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1281-:d:393949
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/8/1281/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/8/1281/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Na Zhang & Fengde Chen & Qianqian Su & Ting Wu, 2011. "Dynamic Behaviors of a Harvesting Leslie-Gower Predator-Prey Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-14, April.
    2. Xiangdong Xie & Fengde Chen & Yalong Xue, 2014. "Note on the Stability Property of a Cooperative System Incorporating Harvesting," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-5, April.
    Full references (including those not matched with items on IDEAS)

    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. Qiu, Huanhuan & Guo, Shangjiang, 2019. "Steady-states of a Leslie–Gower model with diffusion and advection," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 695-709.
    2. Cortés García, Christian, 2023. "Impact of prey refuge in a discontinuous Leslie-Gower model with harvesting and alternative food for predators and linear functional response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 147-165.

    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:8:y:2020:i:8:p:1281-:d:393949. 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.