Persistence criteria for a chemostat with variable nutrient input

Abstract

The standard single-species chemostat model is modified to include a variable nutrient input which is assumed only to be nonnegative, bounded, and continuous. We obtain necessary and sufficient conditions for persistence and show that all solutions of any given chemostat system have the same long-time behavior independent of the initial conditions. Counterexamples shed light on the results obtained. © 2001 Academic Press.