IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v232y2025icp227-244.html
   My bibliography  Save this article

Dynamic complexity of Holling-Tanner predator–prey system with predator cannibalism

Author

Listed:
  • Zhao, Zhihong
  • Shen, Yuwei

Abstract

Cannibalism is a common intraspecific interaction phenomenon and thus the elucidation of the mechanisms of cannibalism can enrich the ecological dynamics. In this paper, we investigate a Holling-Tanner system with predator cannibalism, which is rarely studied. For the non-spatial system, the local dynamics of the origin are fully characterized. The global dynamics of the constant positive steady state, including global stability, Hopf bifurcation and its directions, are examined. For the diffusion system, the Turing instability and global asymptotic stability for the constant steady state are derived, and the existence of Hopf bifurcation and Turing–Hopf bifurcation are studied. We found that predator cannibalism not only leads to complex dynamical behaviors around the origin in non-spatial system, but influences the global asymptotically stability and Turing instability of E∗, as well as results in Hopf bifurcation and Turing–Hopf bifurcation of diffusion system, which can reveal the reasons for the effects of predator cannibalism on biological systems. The numerical verification of the obtained results, the evaluation of the impact of predator cannibalism on the dynamics are also presented.

Suggested Citation

  • Zhao, Zhihong & Shen, Yuwei, 2025. "Dynamic complexity of Holling-Tanner predator–prey system with predator cannibalism," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 232(C), pages 227-244.
    • Handle: RePEc:eee:matcom:v:232:y:2025:i:c:p:227-244
    DOI: 10.1016/j.matcom.2024.12.025
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475424005093
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2024.12.025?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. Banerjee, Malay & Zhang, Lai, 2014. "Influence of discrete delay on pattern formation in a ratio-dependent prey–predator model," Chaos, Solitons & Fractals, Elsevier, vol. 67(C), pages 73-81.
    2. Roshan K. Vijendravarma & Sunitha Narasimha & Tadeusz J. Kawecki, 2013. "Predatory cannibalism in Drosophila melanogaster larvae," Nature Communications, Nature, vol. 4(1), pages 1-8, June.
    3. Sajan, & Anshu, & Dubey, Balram, 2024. "Study of a cannibalistic prey–predator model with Allee effect in prey under the presence of diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    4. Li, Yajing & He, Mengxin & Li, Zhong, 2022. "Dynamics of a ratio-dependent Leslie–Gower predator–prey model with Allee effect and fear effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 417-439.
    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. Chang, Lili & Jin, Zhen, 2018. "Efficient numerical methods for spatially extended population and epidemic models with time delay," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 138-154.
    2. Tian, Canrong & Ling, Zhi & Zhang, Lai, 2017. "Nonlocal interaction driven pattern formation in a prey–predator model," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 73-83.
    3. Emily R Churchill & Calvin Dytham & Jon R Bridle & Michael D F Thom, 2021. "Social and physical environment independently affect oviposition decisions in Drosophila," Behavioral Ecology, International Society for Behavioral Ecology, vol. 32(6), pages 1391-1399.
    4. Chang, Lili & Sun, Gui-Quan & Wang, Zhen & Jin, Zhen, 2015. "Rich dynamics in a spatial predator–prey model with delay," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 540-550.
    5. Tian, Yuan & Li, Huanmeng & Sun, Kaibiao, 2024. "Complex dynamics of a fishery model: Impact of the triple effects of fear, cooperative hunting and intermittent harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 31-48.
    6. Seralan Vinoth & R. Vadivel & Nien-Tsu Hu & Chin-Sheng Chen & Nallappan Gunasekaran, 2023. "Bifurcation Analysis in a Harvested Modified Leslie–Gower Model Incorporated with the Fear Factor and Prey Refuge," Mathematics, MDPI, vol. 11(14), pages 1-25, July.
    7. Zhuo, Xiao-jing & Guo, Yong-feng & Qi, Jing-yan & Wang, Qian-qian, 2024. "Stationary distribution and mean extinction time in a generalist prey–predator model driven by Lévy noises," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    8. Thomas A. Verschut & Renny Ng & Nicolas P. Doubovetzky & Guillaume Calvez & Jan L. Sneep & Adriaan J. Minnaard & Chih-Ying Su & Mikael A. Carlsson & Bregje Wertheim & Jean-Christophe Billeter, 2023. "Aggregation pheromones have a non-linear effect on oviposition behavior in Drosophila melanogaster," Nature Communications, Nature, vol. 14(1), pages 1-15, December.
    9. Chen, Fengde & Li, Zhong & Pan, Qin & Zhu, Qun, 2025. "Bifurcations in a Leslie–Gower predator–prey model with strong Allee effects and constant prey refuges," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
    10. Feng, Xiaozhou & Liu, Xia & Sun, Cong & Jiang, Yaolin, 2023. "Stability and Hopf bifurcation of a modified Leslie–Gower predator–prey model with Smith growth rate and B–D functional response," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

    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:232:y:2025:i:c:p:227-244. 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.