Persistence criteria for a chemostat with variable nutrient input and variable washout with delayed response in growth

RODRIGUEZ CARTABIA, MAURO

CHAOS, SOLITONS AND FRACTALS

PERGAMON-ELSEVIER SCIENCE LTD

Año: 2023 vol. 172

0960-0779

 We study a general single-species chemostat model  with non-autonomous input and washout, and a discrete-time delay between consumption of the nutrient and growth. The goal of this article is to provide sufficient and necessary conditions for persistence. The persistence criteria obtained here extend previous works done for the autonomous model with delay and for the non-autonomous model without delay. Furthermore, in the particular case of periodic nutrient input and the same periodic washout with delayed response in growth, the persistence criteria can be expressed in terms of the average of the involved functions. We remark in no  case we need to impose any restrictions on the size of the delay.