Global dynamics of the chemostat with variable yields

TL;DR

This paper analyzes a multi-species chemostat model with variable yields, demonstrating that under certain conditions, only the species with the lowest break-even concentration persists, using Lyapunov stability methods.

Contribution

It extends chemostat competition analysis to include variable yields and non-monotone responses, providing new stability results.

Findings

Only the species with the lowest break-even concentration survives.

The results apply to models with both monotone and non-monotone response functions.

Lyapunov stability theory is used to establish the main results.

Abstract

In this paper, we consider a competition model between $n$ species in a chemostat including both monotone and non-monotone response functions, distinct removal rates and variable yields. We show that only the species with the lowest break-even concentration survives, provided that additional technical conditions on the growth functions and yields are satisfied. LaSalle's extension theorem of the Lyapunov stability theory is the main tool.