Competition in the nutrient-driven self-cycling fermentation process

TL;DR

This paper models nutrient-driven self-cycling fermentation with impulsive differential equations, demonstrating conditions for coexistence of multiple microbial species, contrasting with traditional chemostat models.

Contribution

It introduces a novel impulsive differential equation model for self-cycling fermentation and proves conditions for species coexistence, including numerical evidence for three-species coexistence.

Findings

Two species can coexist under certain conditions.

Numerical simulations suggest three species may coexist.

Coexistence can be mediated by competition in self-cycling fermentation.

Abstract

Self-cycling fermentation is an automated process used for culturing microorganisms. We consider a model of $n$ distinct species competing for a single non-reproducing nutrient in a self-cycling fermentor in which the nutrient level is used as the decanting condition. The model is formulated in terms of impulsive ordinary differential equations. We prove that two species are able to coexist in the fermentor under certain conditions. We also provide numerical simulations that suggest coexistence of three species is possible and that competitor-mediated coexistence can occur in this case. These results are in contrast to the chemostat, the continuous analogue, where multiple species cannot coexist on a single nonreproducing nutrient.