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

Miled El Hajji 1 Alain Rapaport 1, 2
1 MERE - Water Resource Modeling
CRISAM - Inria Sophia Antipolis - Méditerranée , INRA - Institut National de la Recherche Agronomique : UMR0729
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.
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https://hal.inria.fr/hal-00858543
Contributor : Alain Rapaport <>
Submitted on : Thursday, September 5, 2013 - 3:37:09 PM
Last modification on : Thursday, July 2, 2020 - 2:17:26 PM

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Miled El Hajji, Alain Rapaport. Practical coexistence of two species in the chemostat - A slow-fast characterization. Mathematical Biosciences, Elsevier, 2009, 218 (1), pp.33-39. ⟨10.1016/j.mbs.2008.12.003⟩. ⟨hal-00858543⟩

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