Propagation Phenomena for a Discrete Diffusive Predator–Prey Model in a Shifting Habitat

This paper concerns a discrete diffusive predator–prey system involving two competing predators and one prey in a shifting habitat induced by the climate change. By assuming that both predators can increase when the prey is at the maximal capacity and the prey can still survive under optimal climatic conditions when these two predators have their maximal densities, we investigate the existence and non-existence for different types of forced traveling waves which describe the conversion from the state of a saturated aboriginal prey with two invading alien predators, an aboriginal co-existent predator–prey with an invading alien predator, and the coexistence of three species to the extinction state, respectively. The existence of supercritical and critical forced waves is showed by applying Schauder’s fixed point theorem on various invariant cones via constructing different types of generalized super- and sub-solutions while the non-existence of subcritical forced waves is obtained by contradiction.