An impulsive reaction-diffusion model with asymptotically bounded domain

In this paper, we propose a continuous-discrete hybrid population model in a time-varying and asymptotically bounded domain. For the sake of analysis, this model is transformed into an impulsive reaction-diffusion system in a fixed domain. With the aid of the discrete-time semiflow generated by the solution maps of a limiting system and the theory of chain transitive sets, we establish the threshold-type results on the global dynamics of the model system in the cases of monotone and nonmonotone birth functions, respectively. Our explicit formula of the threshold value can help to understand how the final expansion factor of the habitat and the birth pulse rate affect the survival of population.