Spatial dynamics of some modified Leslie-Gower prey-predator model with shifting habitat

Abstract

In this paper, we will mainly study the spatial dynamics of a modified Leslie-Gower prey-predator model in a shifting habitat. The main concerns are the extinction and persistent conditions under the interaction between two species with different dispersal speed comparing with the shifting habitat edge constant c. We will complete the proof of the persistent conditions in different case of spreading speed. At the same time, we establish the coexist condition of the prey and predator. In the last, their corresponding numerical simulations are also given to illustrate the analytical conclusions.