  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.
