The buffered chemostat with non-monotonic response functions

TL;DR

This paper investigates how a buffer in a chemostat model affects species persistence and stability, especially with non-monotonic response functions, revealing configurations that ensure global stability unlike simpler vessel arrangements.

Contribution

It characterizes buffered configurations that guarantee global stability in chemostats with non-monotonic response functions, highlighting the impact of spatial structure on ecological dynamics.

Findings

Buffer can enable species persistence or extinction depending on its characteristics.

Buffered configurations can achieve global stability with non-monotonic response functions.

Single, serial, or parallel vessels cannot ensure global stability under the same conditions.

Abstract

We study how a particular spatial structure with a buffer impacts the number of equilibria and their stability in the chemostat model. We show that the occurrence of a buffer can allow a species to persist or on the opposite to go extinct, depending on the characteristics of the buffer. For non-monotonic response functions, we characterize the buffered configurations that make the chemostat dynamics globally asymptotically stable, while this is not possible with single, serial or parallel vessels of the same total volume and input flow. These results are illustrated with the Haldane kinetic function.