Effects of impulsive harvesting and an evolving domain in a diffusive logistic model

TL;DR

This paper investigates how domain evolution and impulsive harvesting influence population dynamics using a diffusive logistic model, revealing that domain growth can enhance survival while harvesting can cause extinction.

Contribution

It introduces an explicit ecological reproduction index for a population model on evolving domains with impulsive harvesting, and analyzes its threshold dynamics.

Findings

Large domain evolution rate promotes population survival.

Impulsive harvesting can lead to population extinction.

Numerical simulations support theoretical results.

Abstract

In order to understand how the combination of domain evolution and impulsive harvesting affect the dynamics of a population, we propose a diffusive logistic population model with impulsive harvesting on a periodically evolving domain. Initially the ecological reproduction index of the impulsive problem is introduced and given by an explicit formula, which depends on the domain evolution rate and the impulsive function. Then the threshold dynamics of the population under monotone or nonmonotone impulsive harvesting is established based on this index. Finally numerical simulations are carried out to illustrate our theoretical results, and reveal that a large domain evolution rate can improve the population survival, no matter which impulsive harvesting takes place. Contrary, impulsive harvesting has a negative effect on the population survival, and can even lead to the extinction of the population.