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Dynamics of a ratio-dependent Leslie–Gower predator–prey model with Allee effect and fear effect

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  • Li, Yajing
  • He, Mengxin
  • Li, Zhong

Abstract

We propose a ratio-dependent Leslie–Gower predator–prey model with the Allee effect and fear effect on prey and study its dynamic behaviors. On the basis of Poincaré transformation and blow-up method, we find that the solutions of the system are bounded and the origin is attractive. We consider the existence of equilibria and analyze their stability. The bifurcation of the system was analyzed, including the occurrence of saddle–node bifurcation, degenerate Hopf bifurcation, and Bogdanov–Takens bifurcation. The results show that the system has a cusp of codimension two and undergoes a Bogdanov–Takens bifurcation of codimension two. Numerical simulation results show that there exist two limit cycles (the inner one is stable and the outer one is unstable) and a Bogdanov–Takens bifurcation of codimension two in the system.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:201:y:2022:i:c:p:417-439
    DOI: 10.1016/j.matcom.2022.05.017
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    References listed on IDEAS

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    1. Arancibia–Ibarra, Claudio & Flores, José, 2021. "Dynamics of a Leslie–Gower predator–prey model with Holling type II functional response, Allee effect and a generalist predator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 1-22.
    2. Panday, Pijush & Samanta, Sudip & Pal, Nikhil & Chattopadhyay, Joydev, 2020. "Delay induced multiple stability switch and chaos in a predator–prey model with fear effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 134-158.
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    Cited by:

    1. 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.
    2. 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).
    3. 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.

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