Radhouane Fekih-Salem ; Tewfik Sari - Operating diagram of a flocculation model in the chemostat

arima:5593 - Revue Africaine de Recherche en Informatique et Mathématiques Appliquées, August 7, 2020, Volume 31 - 2019 - CARI 2018 - https://doi.org/10.46298/arima.5593
Operating diagram of a flocculation model in the chemostatArticle

Authors: Radhouane Fekih-Salem ORCID1,2; Tewfik Sari ORCID3

  • 1 Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis]
  • 2 Institut Supérieur d’Informatique de Mahdia
  • 3 Information – Technologies – Analyse Environnementale – Procédés Agricoles

The objective of this study is to analyze a model of the chemostat involving the attachment and detachment dynamics of planktonic and aggregated biomass in the presence of a single resource. Considering the mortality of species, we give a complete analysis for the existence and local stability of all steady states for general monotonic growth rates. The model exhibits a rich set of behaviors with a multiplicity of coexistence steady states, bi-stability, and occurrence of stable limit cycles. Moreover, we determine the operating diagram which depicts the asymptotic behavior of the system with respect to control parameters. It shows the emergence of a bi-stability region through a saddle-node bifurcation and the occurrence of coexistence region through a transcritical bifurcation. Finally, we illustrate the importance of the mortality on the destabilization of the microbial ecosystem by promoting the washout of species.

Volume: Volume 31 - 2019 - CARI 2018
Published on: August 7, 2020
Accepted on: July 28, 2020
Submitted on: June 21, 2019
Keywords: Bi-stability,Bifurcation,Chemostat,Flocculation,Operating diagram,Bi-stabilité,Bifurcation,Chémostat,Floculation,Diagramme opératoire,[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS],[SDE]Environmental Sciences

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