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

Abstract

In order to understand how the combination of the evolution of a domain and impulsive harvesting affect the dynamics of a population, we investigate 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 subject to monotone or nonmonotone impulsive harvesting are established based on this index. Finally numerical simulations are carried out to illustrate our theoretical results, and these reveal that a large domain evolution rate can improve the populations ability to survive, no matter which impulsive harvesting takes place. On the contrary, impulsive harvesting has a negative effect on the survival of the population, and can even lead to its extinction.