publication . Conference object . 2017

Analyse d'un modèle de floculation dans le chemostat

Sari, T.; Fekih Salem, R.;
Open Access English
  • Published: 10 May 2017
  • Publisher: ENIT-LAMSIN
Abstract
8ème colloque - Tendances dans les Applications Mathématiques en Tunisie, Algérie et Maroc, Hammamet, TUN, 10-/05/2017 - 13/05/2017; International audience; A model of the chemostat involving planktonic and attached bacteria competing for a single nutrient is considered. We study this flocculation model with monotonic growth rates and same removal rates. We show that this model has at most one positive steady state that is stable as long as it exists where planktonic and attached bacteria can coexist. According to control parameters, the operating diagram illustrates the washout and coexistence regions that depend only on the growth rate of planktonic bacteria. ...
Subjects
free text keywords: bacteria, MICROBIOLOGIE, MODELISATION, microbiology, BACTERIE, [SDE]Environmental Sciences, FLOCULATION, flocculation, modelling, chemostat

[1] J. COSTERTON “Overview of microbial biofilms“, J. Indust. Microbiol., vol. 15, 137-140, 1995.

[2] R. FEKIH-SALEM, “Modèles mathématiques pour la compétition et la coexistence des espèces microbiennes dans un chémostat“, (Ph.D. thesis), University of Montpellier 2 and University of Tunis el Manar, 2013. ❤!!♣#✿✴✴!❡❧✳❛*❝❤✐✈❡#✲♦✉✈❡*!❡#✳❢*✴!❡❧✲✵✶✵✶✽✻✵✵ .

[3] R. FEKIH-SALEM, J. HARMAND, C. LOBRY, A. RAPAPORT, T. SARI, “Extensions of the chemostat model with flocculation”, J. Math. Anal. Appl., vol. 397, 292-306, 2013. [OpenAIRE]

[4] R. FEKIH-SALEM, A. RAPAPORT, T. SARI, “Emergence of coexistence and limit cycles in the chemostat model with flocculation for a general class of functional responses”, Appl. Math. Modell., vol. 40, 7656-7677, 2016. [OpenAIRE]

[5] S.R. HANSEN, S.P. HUBBELL, “Single-nutrient microbial competition: qualitative agreement between experimental and theoretically forecast outcomes”, Science, vol. 207, 1491-1493, 1980.

[6] J. HARMAND, C. LOBRY, A. RAPAPORT, T. SARI, “Le Chémostat: Théorie Mathématique de la Culture Continue de Micro-organismes”, ISTE Editions Collection Génie des Procédés, Série Chémostat et bioprocédés, Vol. 1, 2017.

[7] B. HAEGEMAN, A. RAPAPORT, “How flocculation can explain coexistence in the chemostat”, J. Biol. Dyn., vol. 2, 1-13, 2008. [OpenAIRE]

[8] H.L. SMITH, P. WALTMAN, “The Theory of the Chemostat, Dynamics of Microbial Competition ”, Cambridge University Press, 1995.

[9] D.N. THOMAS, S.J. JUDD, N. FAWCETT, “Flocculation modelling: a review”, Water Res., vol. 33, 1579-1592, 1999.

Similar Outcomes
Abstract
8ème colloque - Tendances dans les Applications Mathématiques en Tunisie, Algérie et Maroc, Hammamet, TUN, 10-/05/2017 - 13/05/2017; International audience; A model of the chemostat involving planktonic and attached bacteria competing for a single nutrient is considered. We study this flocculation model with monotonic growth rates and same removal rates. We show that this model has at most one positive steady state that is stable as long as it exists where planktonic and attached bacteria can coexist. According to control parameters, the operating diagram illustrates the washout and coexistence regions that depend only on the growth rate of planktonic bacteria. ...
Subjects
free text keywords: bacteria, MICROBIOLOGIE, MODELISATION, microbiology, BACTERIE, [SDE]Environmental Sciences, FLOCULATION, flocculation, modelling, chemostat

[1] J. COSTERTON “Overview of microbial biofilms“, J. Indust. Microbiol., vol. 15, 137-140, 1995.

[2] R. FEKIH-SALEM, “Modèles mathématiques pour la compétition et la coexistence des espèces microbiennes dans un chémostat“, (Ph.D. thesis), University of Montpellier 2 and University of Tunis el Manar, 2013. ❤!!♣#✿✴✴!❡❧✳❛*❝❤✐✈❡#✲♦✉✈❡*!❡#✳❢*✴!❡❧✲✵✶✵✶✽✻✵✵ .

[3] R. FEKIH-SALEM, J. HARMAND, C. LOBRY, A. RAPAPORT, T. SARI, “Extensions of the chemostat model with flocculation”, J. Math. Anal. Appl., vol. 397, 292-306, 2013. [OpenAIRE]

[4] R. FEKIH-SALEM, A. RAPAPORT, T. SARI, “Emergence of coexistence and limit cycles in the chemostat model with flocculation for a general class of functional responses”, Appl. Math. Modell., vol. 40, 7656-7677, 2016. [OpenAIRE]

[5] S.R. HANSEN, S.P. HUBBELL, “Single-nutrient microbial competition: qualitative agreement between experimental and theoretically forecast outcomes”, Science, vol. 207, 1491-1493, 1980.

[6] J. HARMAND, C. LOBRY, A. RAPAPORT, T. SARI, “Le Chémostat: Théorie Mathématique de la Culture Continue de Micro-organismes”, ISTE Editions Collection Génie des Procédés, Série Chémostat et bioprocédés, Vol. 1, 2017.

[7] B. HAEGEMAN, A. RAPAPORT, “How flocculation can explain coexistence in the chemostat”, J. Biol. Dyn., vol. 2, 1-13, 2008. [OpenAIRE]

[8] H.L. SMITH, P. WALTMAN, “The Theory of the Chemostat, Dynamics of Microbial Competition ”, Cambridge University Press, 1995.

[9] D.N. THOMAS, S.J. JUDD, N. FAWCETT, “Flocculation modelling: a review”, Water Res., vol. 33, 1579-1592, 1999.

Similar Outcomes
Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue
publication . Conference object . 2017

Analyse d'un modèle de floculation dans le chemostat

Sari, T.; Fekih Salem, R.;