 
Summary: CANADIAN APPLIED
MATHEMATICS QUARTERLY
Volume 11, Number 2, Summer 2003
CONSIDERATIONS ON YIELD, NUTRIENT
UPTAKE, CELLULAR GROWTH, AND
COMPETITION IN CHEMOSTAT MODELS
JULIEN ARINO, SERGEI S. PILYUGIN
AND GAIL S. K. WOLKOWICZ
ABSTRACT. We investigate some properties of a very gen
eral model of growth in the chemostat. In the classical mod
els of the chemostat, the function describing cellular growth
is assumed to be a constant multiple of the function modeling
substrate uptake. The constant of proportionality is called the
growth yield constant. Here, this assumption of a constant de
scribing growth yield is relaxed. Instead, we assume that the
relationship between uptake and growth might depend on the
substrate concentration and hence that the yield is variable.
We obtain criteria for the stability of equilibria and for the
occurrence of a Hopf bifurcation. In particular, a Hopf bifur
cation can occur if the uptake function is unimodal. Then, in
