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Dynamics of a Leslie–Gower type predator–prey system with herd behavior and constant harvesting in prey

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  • Yao, Yong

Abstract

In this paper, the dynamics of a Leslie–Gower type predator–prey system with herd behavior and constant harvesting in prey are investigated. Earlier work has shown that the herd behavior in prey merely induces a supercritical Hopf bifurcation in the classic Leslie–Gower predator–prey system in the absence of harvesting. However, the work in this paper shows that the presence of herd behavior and constant harvesting in prey can give rise to numerous kinds of bifurcation at the non-hyperbolic equilibria in the classic Leslie–Gower predator–prey system such as two saddle–node bifurcations and one Bogdanov–Takens bifurcation of codimension two at the degenerate equilibria and one degenerate Hopf bifurcation of codimension three at the weak focus. Some numerical simulations are also provided to verify the theoretical results and evaluate their biological implications such as the changes of phase diagram near the degenerate equilibrium due to the Bogdanov–Takens bifurcation and the coexistence of multiple limit cycles arising from the degenerate Hopf bifurcation. Hence, the research results reveal that the herd behavior and constant harvesting in prey have a strong influence on the dynamics and also contribute to promoting the ecological diversity and maintaining the long-term economic benefits.

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  • Yao, Yong, 2025. "Dynamics of a Leslie–Gower type predator–prey system with herd behavior and constant harvesting in prey," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 229(C), pages 32-49.
    • Handle: RePEc:eee:matcom:v:229:y:2025:i:c:p:32-49
    DOI: 10.1016/j.matcom.2024.09.026
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    References listed on IDEAS

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    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. Shang, Zuchong & Qiao, Yuanhua & Duan, Lijuan & Miao, Jun, 2021. "Bifurcation analysis in a predator–prey system with an increasing functional response and constant-yield prey harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 976-1002.
    3. Mandal, Gourav & Guin, Lakshmi Narayan & Chakravarty, Santabrata & Rojas-Palma, Alejandro & González-Olivares, Eduardo, 2024. "Allee-induced bubbling phenomena in an interacting species model," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    4. Kumar, Sachin & Kharbanda, Harsha, 2019. "Chaotic behavior of predator-prey model with group defense and non-linear harvesting in prey," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 19-28.
    5. Mortuja, Md Golam & Chaube, Mithilesh Kumar & Kumar, Santosh, 2021. "Dynamic analysis of a predator-prey system with nonlinear prey harvesting and square root functional response," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
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