A new proof of the competitive exclusion principle in the chemostat

TL;DR

This paper presents a new, elementary proof of the competitive exclusion principle in the chemostat model, applicable to any set of increasing growth functions, using induction and ODE comparisons.

Contribution

It introduces a novel proof method for the competitive exclusion principle in the chemostat, applicable to general growth functions and based on elementary analysis.

Findings

Proof applies to any increasing growth functions

Uses induction on the number of species

Employs elementary ODE analysis

Abstract

We give an new proof of the well-known competitive exclusion principle in the chemostat model with $n$ species competing for a single resource, for any set of increasing growth functions. The proof is constructed by induction on the number of the species, after being ordered. It uses elementary analysis and comparisons of solutions of ordinary differential equations.