Stability analysis of a self-cycling fermentation model with state-dependent impulse times

Abstract

A self-cycling fermenter is a batch fermenter subject to recurrent emptyings of liquid volume followed by the refillingwith new fresh substrate. This article constructs amodified model of self-cycling fermenter, which is described by an impulsive differential equation at impulse-dependent times, which have been recently introduced. The main result is a set of conditions depending of the fraction of removed volume, the concentration of new substrate introduced, and the maximal length between two impulses, which ensure the existence and attractiveness of a periodic cycle. A second result provides alternative conditions for the biomass extinction.