Spatial dynamics of some modified Leslie-Gower prey-predator model in time-periodic shifting environments

In this paper, we will mainly study the spatial dynamics of the Leslie-Gower prey-predator model in time-periodic shifting environments. By using the squeezing technique and the upper-lower solution method, we first establish the existence of time-periodic forced waves connecting the extinction state to the co-existence state or connecting the extinction state to itself. Then, we discuss the spreading properties of this model. We concern the extinction and persistent conditions of two species under different ranges of the shifting habitat edge constant $ c $. Finally, we give some numerical simulations to illustrate the analytical results.