Global dynamics of competition models with nonsymmetric nonlocal dispersals when one diffusion rate is small

TL;DR

This paper investigates the global behavior of two-species competition models with nonsymmetric nonlocal dispersal, showing that local stability leads to global stability when one diffusion rate is sufficiently small, extending previous symmetric cases.

Contribution

It extends prior work on symmetric nonlocal dispersal to nonsymmetric cases, establishing conditions under which local stability implies global stability.

Findings

Local stability implies global stability with small diffusion rate

Results extend symmetric dispersal models to nonsymmetric cases

Provides theoretical insights into competition dynamics with nonlocal dispersal

Abstract

In this paper, we study the global dynamics of a general $2\times 2$ competition models with nonsymmetric nonlocal dispersal operators. Our results indicate that local stability implies global stability provided that one of the diffusion rates is sufficiently small. This paper continues the work in \cite{BaiLi2017}, where competition models with symmetric nonlocal operators are considered.