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Dynamics of a Discrete Leslie–Gower Model with Harvesting and Holling-II Functional Response

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  • Chen Zhang

    (Department of Big Data Science, School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China)

  • Xianyi Li

    (Department of Big Data Science, School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China)

Abstract

Recently, Christian Cortés García proposed and studied a continuous modified Leslie–Gower model with harvesting and alternative food for predator and Holling-II functional response, and proved that the model undergoes transcritical bifurcation, saddle-node bifurcation and Hopf bifurcation. In this paper, we dedicate ourselves to investigating the bifurcation problems of the discrete version of the model by using the Center Manifold Theorem and bifurcation theory, and obtain sufficient conditions for the occurrences of the transcritical bifurcation and Neimark–Sacker bifurcation, and the stability of the closed orbits bifurcated. Our numerical simulations not only illustrate corresponding theoretical results, but also reveal new dynamic chaos occurring, which is an essential difference between the continuous system and its corresponding discrete version.

Suggested Citation

  • Chen Zhang & Xianyi Li, 2023. "Dynamics of a Discrete Leslie–Gower Model with Harvesting and Holling-II Functional Response," Mathematics, MDPI, vol. 11(15), pages 1-19, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3303-:d:1203921
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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. Baogui Xin & Zhiheng Wu, 2015. "Neimark–Sacker Bifurcation Analysis and 0–1 Chaos Test of an Interactions Model between Industrial Production and Environmental Quality in a Closed Area," Sustainability, MDPI, vol. 7(8), pages 1-19, July.
    3. Zhang, Huisen & Cai, Yongli & Fu, Shengmao & Wang, Weiming, 2019. "Impact of the fear effect in a prey-predator model incorporating a prey refuge," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 328-337.
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