Minimal wave speed for a predator–prey system with nonlocal dispersal

Abstract

In this paper, we are concerned with the propagation dynamics of a nonlocal dispersal predator–prey model with one predator and two preys. Accurately, we mainly study the invading phenomenon of an alien predator to the habitat of two aborigine preys, which is depicted by traveling waves connecting the predator-free state to the co-existence state. We characterize the minimal wave speed of this invading process based on an application of Schauder’s fixed point theorem with the help of generalized upper-lower solutions and the Lyapunov argument. Particularly, the discussion of traveling waves with critical wave speed is more involved due to the effect of nonlocal dispersal. Finally, a numerical simulation is given to present the traveling waves and shows the differences between non-local and local dispersals.