Dynamics of the logistic harvesting model with infinite delay on periodically evolving domains

Abstract

In order to understand the impact of periodic evolution in habitats on the survival of species, a logistic reaction diffusion harvesting model with infinite delay in a periodically evolving domain is studied. By assuming that the evolving domain is uniform and isotropic, the model is converted into a reaction diffusion problem in a fixed domain. The asymptotic behavior of the model is obtained by using principal eigenvalue and the upper and lower solutions method, and a biological explanation of the impact of regional evolution on species is given. Our theoretical results and numerical simulations show that big evolution rate benefits the survival of species.