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Hopf Bifurcation and Control for the Bioeconomic Predator–Prey Model with Square Root Functional Response and Nonlinear Prey Harvesting

Author

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  • Huangyu Guo

    (School of Mathematics and Statistics, South-Central Minzu University, Wuhan 430074, China
    These authors contributed equally to this work.)

  • Jing Han

    (School of Information Engineering, Wuhan Business University, Wuhan 430056, China
    These authors contributed equally to this work.)

  • Guodong Zhang

    (School of Mathematics and Statistics, South-Central Minzu University, Wuhan 430074, China)

Abstract

In this essay, we introduce a bioeconomic predator–prey model which incorporates the square root functional response and nonlinear prey harvesting. Due to the introduction of nonlinear prey harvesting, the model demonstrates intricate dynamic behaviors in the predator–prey plane. Economic profit serves as a bifurcation parameter for the system. The stability and Hopf bifurcation of the model are discussed through normal forms and bifurcation theory. These results reveal richer dynamic features of the bioeconomic predator–prey model which incorporates the square root functional response and nonlinear prey harvesting, and provides guidance for realistic harvesting. A feedback controller is introduced in this paper to move the system from instability to stability. Moreover, we discuss the biological implications and interpretations of the findings. Finally, the results are validated by numerical simulations.

Suggested Citation

  • Huangyu Guo & Jing Han & Guodong Zhang, 2023. "Hopf Bifurcation and Control for the Bioeconomic Predator–Prey Model with Square Root Functional Response and Nonlinear Prey Harvesting," Mathematics, MDPI, vol. 11(24), pages 1-18, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:24:p:4958-:d:1300397
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    References listed on IDEAS

    as
    1. H. Scott Gordon, 1954. "The Economic Theory of a Common-Property Resource: The Fishery," Journal of Political Economy, University of Chicago Press, vol. 62(2), pages 124-124.
    2. H. Scott Gordon, 1954. "The Economic Theory of a Common-Property Resource: The Fishery," Palgrave Macmillan Books, in: Chennat Gopalakrishnan (ed.), Classic Papers in Natural Resource Economics, chapter 9, pages 178-203, Palgrave Macmillan.
    3. 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).
    4. Li, Huan & Huang, Chengdai & Li, Tongxing, 2019. "Dynamic complexity of a fractional-order predator–prey system with double delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
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