Linear and nonlinear minimal speed selection of traveling waves for a competitive system with nonlocal dispersal

Abstract

In this paper, we study the linear and nonlinear selection of the minimal wave speed of traveling waves for a two-species Lotka-Volterra competitive system with nonlocal diffusion. By using the method of upper-lower solutions, we establish some new conditions for linear and nonlinear minimal speed selection. It is shown that the strong competition between two populations will lead to the realization of nonlinear selection, and the minimal speed selection can be realized linearly under appropriate conditions. Two examples are also presented to illustrate the realization of linear and nonlinear selection.