Persistence Criteria for a Chemostat with Variable Nutrient Input
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.
Ellermeyer, S. F., Pilyugin, S. S., & Redheffer, R. (2001). Persistence criteria for a chemostat with variable nutrient input. Journal of Differential Equations, 171(1), 132-147. doi:10.1006/jdeq.2000.4041