IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v180y2021icp1-23.html
   My bibliography  Save this article

Hopf bifurcation of a multiple-delayed predator–prey system with habitat complexity

Author

Listed:
  • Wang, Shufan
  • Tang, Haopeng
  • Ma, Zhihui

Abstract

This paper proposes a multiple-delayed predator–prey system with habitat complexity and harvesting effort, and investigates the dynamical behavior including stability properties and Hopf bifurcation. Firstly, stability of equilibrium points and the existence of Hopf bifurcation are investigated and some critical conditions which guarantee the corresponding results are obtained based on mathematical view. Secondly, the explicit formulae for determining the direction, stability and period of the bifurcating periodic solutions are derived by using the center manifold theory and the normal form theory. Finally, in order to verify the theoretical results, some numerical simulations are done to illustrate the results. It is observed that the level of abundance of prey and predator populations depends on the gestation delay if the gestation delay exceeds some critical values.

Suggested Citation

  • Wang, Shufan & Tang, Haopeng & Ma, Zhihui, 2021. "Hopf bifurcation of a multiple-delayed predator–prey system with habitat complexity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 1-23.
  • Handle: RePEc:eee:matcom:v:180:y:2021:i:c:p:1-23
    DOI: 10.1016/j.matcom.2020.08.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475420302767
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2020.08.008?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. Li, Yilong & Xiao, Dongmei, 2007. "Bifurcations of a predator–prey system of Holling and Leslie types," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 606-620.
    2. Moghadas, S.M. & Corbett, B.D., 2008. "Limit cycles in a generalized Gause-type predator–prey model," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1343-1355.
    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. Souna, Fethi & Belabbas, Mustapha & Menacer, Youssaf, 2023. "Complex pattern formations induced by the presence of cross-diffusion in a generalized predator–prey model incorporating the Holling type functional response and generalization of habitat complexity e," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 597-618.
    2. Ma, Yuanyuan & Dong, Nan & Liu, Na & Xie, Leilei, 2022. "Spatiotemporal and bifurcation characteristics of a nonlinear prey-predator model," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    3. Ye, Yong & Zhao, Yi & Zhou, Jiaying, 2022. "Promotion of cooperation mechanism on the stability of delay-induced host-generalist parasitoid model," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).

    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. Hu, Guang-Ping & Li, Wan-Tong & Yan, Xiang-Ping, 2009. "Hopf bifurcations in a predator–prey system with multiple delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1273-1285.
    2. Yin, Hongwei & Zhou, Jiaxing & Xiao, Xiaoyong & Wen, Xiaoqing, 2014. "Analysis of a diffusive Leslie–Gower predator–prey model with nonmonotonic functional response," Chaos, Solitons & Fractals, Elsevier, vol. 65(C), pages 51-61.
    3. Chen, Mengxin & Wu, Ranchao, 2023. "Steady states and spatiotemporal evolution of a diffusive predator–prey model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    4. Shang, Zuchong & Qiao, Yuanhua, 2023. "Multiple bifurcations in a predator–prey system of modified Holling and Leslie type with double Allee effect and nonlinear harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 745-764.
    5. Xu, Chaoqun, 2020. "Probabilistic mechanisms of the noise-induced oscillatory transitions in a Leslie type predator-prey model," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    6. Li, Xinxin & Yu, Hengguo & Dai, Chuanjun & Ma, Zengling & Wang, Qi & Zhao, Min, 2021. "Bifurcation analysis of a new aquatic ecological model with aggregation effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 75-96.
    7. Jiao, Xubin & Li, Xiaodi & Yang, Youping, 2022. "Dynamics and bifurcations of a Filippov Leslie-Gower predator-prey model with group defense and time delay," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    8. Çelik, Canan & Duman, Oktay, 2009. "Allee effect in a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1956-1962.

    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:180:y:2021:i:c:p:1-23. 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.