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Dynamics of a Predator–Prey Model with Impulsive Diffusion and Transient/Nontransient Impulsive Harvesting

Author

Listed:
  • Qi Quan

    (School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China)

  • Xiangjun Dai

    (School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China
    School of Date Science, Tongren University, Tongren 554300, China)

  • Jianjun Jiao

    (School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China
    School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China)

Abstract

Harvesting is one of the ways for humans to realize economic interests, while unrestricted harvesting will lead to the extinction of populations. This paper proposes a predator–prey model with impulsive diffusion and transient/nontransient impulsive harvesting. In this model, we consider both impulsive harvesting and impulsive diffusion; additionally, predator and prey are harvested simultaneously. First, we obtain the subsystems of the system in prey extinction and predator extinction. We obtain the fixed points of the subsystems by the stroboscopic map theories of impulsive differential equations and analyze their stabilities. Further, we establish the globally asymptotically stable conditions for the prey/predator-extinction periodic solution and the trivial solution of the system, and then the sufficient conditions for the permanence of the system are given. We also perform several numerical simulations to substantiate our results. It is shown that the transient and nontransient impulsive harvesting have strong impacts on the persistence of the predator–prey model.

Suggested Citation

  • Qi Quan & Xiangjun Dai & Jianjun Jiao, 2023. "Dynamics of a Predator–Prey Model with Impulsive Diffusion and Transient/Nontransient Impulsive Harvesting," Mathematics, MDPI, vol. 11(14), pages 1-25, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3254-:d:1201508
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    References listed on IDEAS

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    1. Tian, Yuan & Gao, Yan & Sun, Kaibiao, 2022. "Global dynamics analysis of instantaneous harvest fishery model guided by weighted escapement strategy," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Tao, Xiangyu & Zhu, Linhe, 2021. "Study of periodic diffusion and time delay induced spatiotemporal patterns in a predator-prey system," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
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    Cited by:

    1. Zeli Zhou & Jianjun Jiao & Xiangjun Dai & Lin Wu, 2024. "Dynamics of a Predator–Prey System with Impulsive Stocking Prey and Nonlinear Harvesting Predator at Different Moments," Mathematics, MDPI, vol. 12(15), pages 1-21, July.

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