Extensions of the chemostat model with flocculation
type: Item
instance of: scholarly article
title: Extensions of the chemostat model with flocculation
zbMATH Open document ID: 1275.92014
published in: Journal of Mathematical Analysis and Applications
publication date: 2012-10-29T00:00:00Z
full work available at URL: https://arxiv.org/abs/1106.6038
review text: In this work a model of the chemostat is studied in the case when the species are presented in two forms, isolated and aggregated individuals, such as attached bacteria or bacteria in flocks. More precisely, general model is considered of a bio-process with three compartments involving the substrate, the planktonic and attached biomass densities, respectively. Each compartment of the biomass is characterized by its own specific growth rate and apparent dilution rate, generalizing previous models of biofilms (with no dilution rate for the attached bacteria) or models of perfect flocks (with no growth rate for aggregated individuals). A class of models with planktonic and structured biomass is analyzed under the assumptions that attachment and detachment processes are fast compared to the biological scale. Assuming that the flocculation and deflocculation dynamics is fast compared to the growth of the species, a reduced chemostat-like model is constructed in which both the growth functions and the apparent dilution rate depend on the density of the species. In the case when the previous assumption is not fulfilled, the analysis of the original three order model must be done to establish its qualitative behavior. The study performed in the paper reveals two main characteristics of this model: the reduced dynamics may exhibit a bi-stable behavior even though each growth function is monotonic. This phenomenon seems to be new and is met in the chemostat but when the growth function is non-monotonic. For bio-processes in which part of the biomass is under a structured form (in flocks or bio films), the macroscopic models (with reduced dynamics involving only the aggregated biomass and the substrate) should include a growth rate and an apparent dilution rate that are both density dependent.
reviewed by: Vasile Dragan
Mathematics Subject Classification ID: 92C37
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 37N25
zbMATH DE Number: 6099601
zbMATH Keywords: density dependent growth functions
zbMATH Keywords: floculation dynamics
zbMATH Keywords: defloculation dynamics
zbMATH Keywords: bio-processes
zbMATH Keywords: bio-films
author: Radhouane Fekih-Salem
author: Jérôme Harmand
author: Claude Lobry
author: A. Rapaport
author: Tewfik Sari
MaRDI profile type: Publication
OpenAlex ID: W2019635403
arXiv ID: 1106.6038
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DOI: 10.1016/J.JMAA.2012.07.055
description: scientific article