Propagation phenomena for a discrete diffusive predator-prey model in a shifting habitat (Q6612574)

This paper investigates a discrete diffusive predator-prey system involving two competing predators and a single prey species in a habitat that is shifting due to climate change. The model assumes that both predators can thrive when the prey reaches its maximum population, and that the prey can survive under optimal climatic conditions even when both predators reach their maximal densities. The study examines the existence and non-existence of different types of forced traveling waves, which describe the transition from various ecological states. These states include: a saturated prey population with two invading predators, a state where an indigenous predator-prey system coexists with an invading alien predator, and the coexistence of all three species leading to extinction. The paper demonstrates the existence of supercritical and critical forced waves by applying Schauder fixed-point theorem on various invariant cones, constructing different generalized super- and sub-solutions. Additionally, the non-existence of subcritical forced waves is established through a proof by contradiction.