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Dynamics of Stage-Structured Predator–Prey Model with Beddington–DeAngelis Functional Response and Harvesting

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  • Haiyin Li

    (Department of Mathematics and Information, Henan University of Economics and Law, Zhengzhou 450046, China)

  • Xuhua Cheng

    (School of Science, Hebei University of Technology, Tianjin 300401, China)

Abstract

In this paper, we investigate the stability of equilibrium in the stage-structured and density-dependent predator–prey system with Beddington–DeAngelis functional response. First, by checking the sign of the real part for eigenvalue, local stability of origin equilibrium and boundary equilibrium are studied. Second, we explore the local stability of the positive equilibrium for τ = 0 and τ ≠ 0 (time delay τ is the time taken from immaturity to maturity predator), which shows that local stability of the positive equilibrium is dependent on parameter τ . Third, we qualitatively analyze global asymptotical stability of the positive equilibrium. Based on stability theory of periodic solutions, global asymptotical stability of the positive equilibrium is obtained when τ = 0 ; by constructing Lyapunov functions, we conclude that the positive equilibrium is also globally asymptotically stable when τ ≠ 0 . Finally, examples with numerical simulations are given to illustrate the obtained results.

Suggested Citation

  • Haiyin Li & Xuhua Cheng, 2021. "Dynamics of Stage-Structured Predator–Prey Model with Beddington–DeAngelis Functional Response and Harvesting," Mathematics, MDPI, vol. 9(17), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2169-:d:629476
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    References listed on IDEAS

    as
    1. Zhao, Xin & Zeng, Zhijun, 2020. "Stationary distribution of a stochastic predator–prey system with stage structure for prey," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    2. 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).
    3. Zhao, Xin & Zeng, Zhijun, 2020. "Stationary distribution and extinction of a stochastic ratio-dependent predator–prey system with stage structure for the predator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
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