Traveling Wavefronts of Competing Pioneer and Climax Model with Nonlocal Diffusion

Abstract

We study a competing pioneer-climax species model with nonlocal diffusion. By constructing a pair of upper-lower solutions and using the iterative technique, we establish the existence of traveling wavefronts connecting the pioneer-existence equilibrium and the coexistence equilibrium. We also discuss the asymptotic behavior of the wave tail for the traveling wavefronts as $s=x+ct\to -\infty$.