Analysis of a Chemostat Model with Quadratic Variable Yield Coefficient

Abstract

We investigate a chemostat model in which the growth rate is given by a Monod expression with a quadratic variable yield coefficient. The
model with linear variable yield coefficient has been investigated by previous researchers using numerical integration. We combine analytical
results with path-following methods. The conditions for washout to occur are found. When washout does not occur we establish the conditions
under which the reactor performance is maximised at either a finite or infinite residence time. We also determine the parameter region in
which oscillations may be generated in the reactor. Computer algebra system MATHEMATICA is used extensively for algebraic and
numerical simulations.