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Stochastic models of the chemostat

Fabien Campillo 1, * Marc Joannides 1, 2 Irène Larramendy 2 
* Corresponding author
1 MERE - Water Resource Modeling
CRISAM - Inria Sophia Antipolis - Méditerranée , INRA - Institut National de la Recherche Agronomique : UMR0729
Abstract : We consider the modeling of the dynamics of the chemostat at its very source. The chemostat is classically represented as a system of ordinary differential equations. Our goal is to establish a stochastic model that is valid at the scale immediately preceding the one corresponding to the deterministic model. At a microscopic scale we present a pure jump stochastic model that gives rise, at the macroscopic scale, to the ordinary differential equation model. At an intermediate scale, an approximation diffusion allows us to propose a model in the form of a system of stochastic differential equations. We expound the mechanism to switch from one model to another, together with the associated simulation procedures. We also describe the domain of validity of the different models.
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https://hal.inria.fr/inria-00537886
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Submitted on : Tuesday, July 5, 2011 - 8:39:16 AM
Last modification on : Saturday, June 25, 2022 - 9:38:34 AM
Long-term archiving on: : Thursday, October 6, 2011 - 2:20:41 AM

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  • HAL Id : inria-00537886, version 2
  • ARXIV : 1011.5108

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Fabien Campillo, Marc Joannides, Irène Larramendy. Stochastic models of the chemostat. [Research Report] RR-7458, INRIA. 2010, pp.39. ⟨inria-00537886v2⟩

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