Uniqueness and stability of coexistence states in two species models with/without chemotaxis on bounded heterogeneous environments

TL;DR

This paper investigates the conditions under which two competing species can coexist uniquely and stably in heterogeneous environments, considering models with and without chemotaxis, extending previous results on persistence and coexistence.

Contribution

It establishes new conditions for the uniqueness and stability of coexistence states, applicable even to systems without chemotaxis but with spatially varying coefficients.

Findings

Conditions for stable coexistence states identified

Uniqueness of coexistence states proven under certain parameters

Results extend to systems without chemotaxis with spatial heterogeneity

Abstract

The current paper is concerned with the asymptotic dynamics of two species competition systems with/without chemotaxis in heterogeneous media. In the previous work \cite{ITBWS17a}, we find conditions on the parameters in such systems for the persistence of the two species and the existence of positive coexistence states. In this paper, we find conditions on the parameters for the uniqueness and stability of positive coexistence states of such systems. The established results are new even for the two species competition systems without chemotaxis but with space dependent coefficients.