Global dynamics of a general competition diffusion system in spatially heterogeneous environments

TL;DR

This paper investigates how dispersal rates and spatial heterogeneity influence population dynamics in a competition model, establishing conditions for stability of various steady states.

Contribution

It provides new insights into the global stability of competition systems considering spatial heterogeneity and dispersal effects.

Findings

Dispersal rate significantly affects population stability.

Spatial heterogeneity influences coexistence and extinction outcomes.

Conditions for global asymptotic stability are established.

Abstract

In this paper, we study a diffusive Lotka-Volterra competition model under homogeneous Dirichlet boundary conditions. We shall discuss the effects of dispersal rate and spatial heterogeneity on population dynamics. More precisely, we establish the main results about the global asymptotic stability of semitrivial as well as coexistence steady states.