DIMACS TR: 2003-44

Crowding effects promote coexistence in the chemostat

Authors: Patrick De Leenheer, David Angeli and Eduardo Sontag

This paper deals with an almost-global stability result for a particular chemostat model. It deviates from the classical chemostat because crowding effects are taken into consideration. This model can be rewritten as a negative feedback interconnection of two systems which are monotone (as input-output systems). Moreover, these subsystems behave nicely when subject to constant inputs. This allows the use of a particular small-gain theorem which has recently been developed for feedback interconnections of monotone systems. Application of this theorem requires -at least approximate- knowledge of two gain functions associated to the subsystems. It turns out that for the chemostat model proposed here, these approximations can be obtained explicitely and this leads to a sufficient condition for almost-global stability. In addition, we show that coexistence occurs in this model if the crowding effects are large enough.

Paper available at ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-44.ps.gz
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