Dynamics of nonautonomous chemostat models

Abstract

Chemostat models have a long history in the biological sciences as well as in biomathematics. Hitherto most investigations have focused on autonomous systems, that is, with constant parameters, inputs and outputs. In many realistic situations these quantities can vary in time, either deterministically (e.g., periodically) or randomly. They are then non-autonomous dynamical systems for which the usual concepts of autonomous systems do not apply or are too restrictive. The newly developing theory of non-autonomous dynamical systems provides the necessary concepts, in particular that of a non-autonomous pullback attractor. These will be used here to analyze the dynamical behavior of non-autonomous chemostat models with or without wall growth, time dependent delays, variable inputs and outputs. The possibility of over-yielding in non-autonomous chemostats will also be discussed.