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Math Biosci. 2009 Mar;218(1):33-9. doi: 10.1016/j.mbs.2008.12.003. Epub 2008 Dec 25.

Practical coexistence of two species in the chemostat - a slow-fast characterization.

Author information

1
UMR Analyse des Systèmes et Biométrie, INRA, 2 Place Viala, 34060 Montpellier Cedex, France.

Abstract

We show that the chemostat model with two species having different but close break-even concentrations exhibits a slow-fast dynamics. Considering small perturbations about the dilution rate for which break-even concentrations are identical, we use the Fenichel theory to show the coexistence of species for large times. Then we determine the reduced dynamics, which is non-trivial and characterized by the slopes of the growth functions about their break-even concentrations.

PMID:
19141299
DOI:
10.1016/j.mbs.2008.12.003
[Indexed for MEDLINE]

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