The Mutual Inclusion in a Nonlocal Competitive Lotka Volterra System

TL;DR

This paper studies traveling front solutions in a nonlocal Lotka-Volterra system to understand species competition, introducing new methods for existence, uniqueness, and decay rate analysis, showing potential coexistence.

Contribution

It presents novel monotone iteration, sliding domain, and decay analysis methods for nonlocal systems, advancing understanding of species competition dynamics.

Findings

Existence of traveling front solutions established.

Uniqueness of solutions for each propagation speed proved.

Long-term coexistence of competing species demonstrated.

Abstract

We investigate the traveling front solutions of a nonlocal Lotka Volterra system to illustrate the outcome of the competition between two species. The existence of the front solution is obtained through a new monotone iteration scheme, the uniqueness of the front solution corresponding to each propagation speed is proved by sliding domain method adapted to nonlocal systems, and the asymptotic decay rate of the fronts with critical and noncritical wave speeds is derived by a new method, which is different from the single equation case. The results demonstrate that in the long run, two weakly competing species can co-exist.