The Spreading Speed and the Existence of Planar Waves for a Class of Predator-prey System with Nonlocal Diffusion

Abstract

In this paper, we study a predator-prey system with general response function and nonlocal diffusion in high dimensional space and investigate the propagation properties of its solution. More precisely, we study the invasion speed of the predator into habitat of the aborigine prey and obtain the existence of the planar waves by constructing the upper and lower solutions. Finally, we present some numerical simulations to support our results.