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
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.
allows the use of a particular small-gain theorem which has recently been
developed for feedback interconnections of
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
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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