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 refilling with new fresh substrate. This article constructs a modified 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. Copyright © 2013 John Wiley & Sons, Ltd.