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

Qi Quan, Xiangjun Dai and Jianjun Jiao ()
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Qi Quan: School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China
Xiangjun Dai: School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China
Jianjun Jiao: School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China

Mathematics, 2023, vol. 11, issue 14, 1-25

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.

Keywords: impulsive diffusion; transient and non-transient impulsive harvesting; predator–prey model; permanence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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