Spatial dynamics of the lattice Leslie-Gower predator-prey model in time-periodic shifting environments

This paper focuses on the spatial dynamics of a lattice Leslie–Gower predator-prey model in a time-periodic shifting environment. Using the squeezing technique combined with the method of upper and lower solutions, we first establish the existence of periodic forced waves that connect the extinction state to the coexistence state, as well as waves that connect the extinction state to itself. Subsequently, we investigate the spreading properties of the model and analyze conditions for the extinction and persistence of the two species under different ranges of the habitat shifting speed $c$. Finally, we provide several numerical simulations to illustrate the analytical results.