Stability of a Simple Bioreactor Model with a General Growth Function, Bacterial Feed and Death Rate

Biological reactors are employed in industrial applications to break down organic waste. Here we consider the stability of an open loop CSTR, with a general growth rate function, having both a bacterial and substrate feed and a death rate. Reactors with a bacterial feed are important as every reactor after the first in a cascade will have both bacterial and substrate feeds. We show that stability of a critical point is related to the sign of the slope of the growth rate function, when no bacterial feed is present, and to the sign of the slope of a function, being the product of the growth rate function and a function involving the substrate and bacterial feed concentrations, when a bacterial feed is present.