Persistence Criteria for a Chemostat with Variable Nutrient Input

Sean F. Ellermeyer, Kennesaw State University
Sergei S. Pilyugin, University of Florida
Ray Redheffer, University of California - Los Angeles


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.