We study a feedback stabilization problem for a first-order hyperbolic partial differential equation. The problem is inspired by the stabilization of equilibrium age profiles for an age-structured chemostat, using the dilution rate as the control. Two distinguishing features of the problem are that (a) the PDE has a multiplicative (instead of an additive) input and (b) the state is fed back to ...

BACKGROUND Saccharomyces cerevisiae is the most relevant yeast species conducting the alcoholic fermentation that takes place during winemaking. Although the physiology of this model organism has been extensively studied, systematic quantitative physiology studies of this yeast under winemaking conditions are still scarce, thus limiting the understanding of fermentative metabolism of wine yeast...

This paper deals with an almost global stability result for a chemostat model with including effects. The proof relies on a particular small-gain theorem which has recently been developed for feedback interconnections of monotone systems.

When the diatom, Phaeodactylum tricornutum, and the microalga, Dunaliella tertiolecta, are cultured together in a chemostat at dilution factors of approximately 0.5 day-1, the diatom develops the higher population density. At dilution factors above 1.2 day-1 the inability of the diatom to assimilate nutrient as fast as it flows into the chemostat results in the microalga generating the larger p...

The chemostat model has been an important tool in studying intestinal microflora. To date, several competitive exclusion products have been developed from such studies as prophylactic treatment against pathogenic bacteria. A continuous-flow chemostat model of a feral pig was developed using inocula from the cecal contents of a wild boar caught in East Texas. Several strains of antibiotic-sensit...

We show how a particular spatial structure with a buffer globally stabilizes the chemostat dynamics with non-monotonic response function, while this is not possible with single, serial or parallel chemostats of the same total volume and input flow. We give a characterization of the set of such configurations that satisfy this property, as well as the configuration that ensures the best nutrient...

1 Review of competition for a single substrate Paul Waltman’s chemostat-related work has had a large impact in population biology, ecology and bio-engineering. It has motivated and inspired the work of many other authors, including us. It seems appropriate to point out a major open problem which remains unresolved after more than thirty years and to touch on some other issues related to bacteri...