Dynamics of a chemostat with periodic nutrient supply

G. ROBLEDO; P. AMSTER; D. SEPÚLVEDA

Conferencia; ICMC Summer Meeting on Differential Equations; 2020

A model of a one-species chemostat with a periodic input is described by a system of delay differential equations, where the delay represents the interval time between the consumption of nutrient and its metabolization by the microbial species. A necessary and sufficient condition ensuring the existence of a periodic solution is obtained by means of a Poincaré operator method combined with Leray-Schauder degree techniques. In addition, uniqueness shall be proved when the delay is sufficiently small.