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Stochastic modeling of the chemostat

F. Campillo, M. Joannides and I. Larramendy-Valverde

Ecological Modelling, 2011, vol. 222, issue 15, 2676-2689

Abstract: The chemostat is classically represented, at large population scale, as a system of ordinary differential equations. Our goal is to establish a set of stochastic models that are valid at different scales: from the small population scale to 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.

Keywords: Stochastic differential equations; Chemostat; Pure jump process; Diffusion approximation; Tau-leap method; Monte Carlo method; Gillespie algorithm (search for similar items in EconPapers)
Date: 2011
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Handle: RePEc:eee:ecomod:v:222:y:2011:i:15:p:2676-2689