Thr standard single-species chemostat model is modified to include a variab
le nutrient input which is assumed only to be nonnegative, bounded, and con
tinuous. We obtain necessary and sufficient conditions for persistence and
show that ail solutions of any given chemostat system have the same long-ti
me behavior independent of the initial conditions. Counterexamples shed lig
ht on the results obtained. (C) 2001 Academic Press.