Extensions of the chemostat model with flocculation

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Conference object , Report 01 Jan 2013Embargo end date: 01 Jan 2011 France English Publisher:Elsevier BVJournal:Journal of Mathematical Analysis and Applications, volume 397, pages 292-306 (issn: 0022-247X,

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Authors: Fekih-Salem, Radhouane; Harmand, Jérôme; Lobry, Claude; Rapaport, Alain; Sari, Tewfik;

doi: 10.1016/j.jmaa.2012.07.055 , 10.48550/arxiv.1106.6038

arXiv: 1106.6038

Extensions of the chemostat model with flocculation

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Abstract

In this work, we study a model of the chemostat where the species are present in two forms, isolated bacteria and under an aggregated form like attached bacteria or bacteria in flocks. We show that our general model contains a lot of models which were previously considered in the literature. Assuming that flocculation and deflocculation dynamics are fast with respect to the growth of the species, we construct a reduced chemostat-like model in which both the growth functions and the apparent dilution rate depend on the density of the species. We also show that such a model involving monotonic growth rates may exhibit bistability, while it may only occur in the classical chemostat model when the growth rate in non monotonic.

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Keywords

[SDE] Environmental Sciences, Cell biology, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], 34D05, 612, Dynamical Systems (math.DS), 92D25, 93C15, 34D23, DENSITY DEPENDENT GROWTH FUNCTIONS, density dependent growth functions, flocculation, Cell Behavior (q-bio.CB), FOS: Mathematics, Mathematics - Dynamical Systems, defloculation dynamics, Ecology, CHEMOSTAT, bio-films, Dynamical systems in biology, floculation dynamics, SYSTEME DYNAMIQUE, Chemostat, FOS: Biological sciences, [SDE]Environmental Sciences, Qualitative investigation and simulation of ordinary differential equation models, FONCTION MATHEMATIQUE, FLOCCULATION, Quantitative Biology - Cell Behavior, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation, bio-processes

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