A discrete one-species chemostat model with delayed response in the growth and non-constant supply
Authors
P. Amster
M. Rodríguez Cartabia
Abstract
A non-autonomous discrete delayed system for a one-species chemostat based on an Ellermeyer model for the continuous case is studied. Conditions for the persistence or the extinction of the solutions are obtained respectively in terms of the lower and upper Bohl exponents for a scalar linear equation associated to the problem. Furthermore, the condition for persistence also implies the attractiveness, that is, the existence of a bounded solution that attracts all the others. As a special case, when the nutrient supply is $ω$-periodic, the picture is complete: the condition for persistence implies the existence of an attractive non-trivial $ω$-periodic solution, while non-persistence implies extinction.
