Stability of traveling waves in non-cooperative systems with nonlocal dispersal of equal diffusivities

TL;DR

This paper establishes a stability criterion for traveling waves in certain non-cooperative reaction-diffusion systems with nonlocal dispersal, and applies it to ecological and epidemiological models.

Contribution

It provides the first stability theorem for traveling waves in non-cooperative systems with nonlocal dispersal of equal diffusivities.

Findings

Proves a stability theorem based on weighted relative entropy.

Demonstrates stability of traveling waves in ecological models.

Shows stability results applicable to epidemiological systems.

Abstract

In this work, we first prove a stability theorem for traveling waves in a class of non-cooperative reaction-diffusion systems with nonlocal dispersal of equal diffusivities. Our stability criterion is in the sense that the initial perturbation is such that a suitable weighted relative entropy function is bounded and integrable. Then we apply our main theorem to derive the stability of traveling waves for some specific examples of non-cooperative systems arising in ecology and epidemiology.