Spreading Speed in an Integrodifference Predator-Prey System without Comparison Principle

In this paper, we study the spreading speed in an integrodifference system which models invasion of predators into the habitat of the prey. Without the requirement of comparison principle, we construct several auxiliary integrodifference equations and use the results of monotone scalar equations to estimate the spreading speed of the invading predators. We also present some numerical simulations to support our theoretical results and demonstrate that the integrodifference predator-prey system exhibits very complex dynamics. Our theory and numerical results imply that the invasion of predators may have a rough constant speed. Moreover, our numerical simulations indicate that the spatial contact of individuals and the overcompensatory phenomenon of the prey may be conducive to the persistence of nonmonotone biological systems and lead to instability of the predator-free state.