Competition in the nutrient-driven self-cycling fermentation process

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.