N. Abdellatif, R. Fekih-salem, and T. Sari, Competition for a single resource and coexistence of several species in the chemostat, Mathematical Biosciences and Engineering, vol.13, issue.4, pp.631-652, 2016.
DOI : 10.3934/mbe.2016012

D. J. Batstone, J. Keller, I. Angelidaki, S. V. Kalyuzhnyi, S. G. Pavlostathis et al., The IWA Anaerobic Digestion Model No 1 (ADM1), Water Science and Technology, vol.45, issue.10, pp.65-73, 2002.
DOI : 10.2166/wst.2002.0292
URL : http://www.enzyme.chem.msu.ru/ekbio/article/ADM1-WST.pdf

B. Benyahia, T. Sari, B. Cherki, and J. Harmand, Bifurcation and stability analysis of a two step model for monitoring anaerobic digestion processes, Journal of Process Control, vol.22, issue.6, pp.1008-1019, 2012.
DOI : 10.1016/j.jprocont.2012.04.012
URL : https://hal.archives-ouvertes.fr/hal-00777051

O. Bernard, Z. Hadj-sadock, D. Dochain, A. Genovesi, and J. P. Steyer, Dynamical model development and parameter identification for an anaerobic wastewater treatment process, Biotechnology and Bioengineering, vol.29, issue.7, pp.424-438, 2001.
DOI : 10.1016/0043-1354(95)00105-T

A. Bornhöft, R. Hanke-rauschenbach, and K. Sundmacher, Steady-state analysis of the Anaerobic Digestion Model No. 1 (ADM1), Nonlinear Dynamics, vol.63, issue.4, pp.535-549, 2013.
DOI : 10.1007/s11071-010-9722-6

A. Burchard, Substrate degradation by a mutualistic association of two species in the Chemostat, Journal of Mathematical Biology, vol.41, issue.5, pp.465-489, 1994.
DOI : 10.1007/978-3-322-96657-5_4

Y. Daoud, N. Abdellatif, and J. Harmand, Modèles mathématiques de digestion anaérobie : effet de l'hydrolyse sur la production du biogaz, p.74, 2018.

Y. Daoud, N. Abdellatif, T. Sari, and J. Harmand, Steady state analysis of a syntrophic model : The effect of a new input substrate concentration, p.102, 2018.

M. Hajji, J. Harmand, H. Chaker, and C. Lobry, Association between competition and obligate mutualism in a chemostat, Journal of Biological Dynamics, vol.13, issue.6, pp.635-647, 2009.
DOI : 10.1128/MMBR.68.4.745-770.2004
URL : https://hal.archives-ouvertes.fr/hal-00858541

M. Hajji, F. Mazenc, and J. Harmand, A mathematical study of a syntrophic relationship of a model of anaerobic digestion process, Mathematical Biosciences and Engineering, vol.7, issue.3, pp.641-656, 2010.
DOI : 10.3934/mbe.2010.7.641
URL : https://hal.archives-ouvertes.fr/hal-01000455

R. Fekih-salem, N. Abdellatif, T. Sari, and J. Harmand, Analyse mathématique d'un modèle de digestion anaérobie à trois étapes, pp.53-71, 2014.

R. Fekih-salem, N. Abdellatif, and A. Yahmadi, Effect of inhibition on a syntrophic relationship model in the anaerobic digestion process, TAMTAM, vol.2017, issue.103, p.117, 2017.

J. Harmand, C. Lobry, A. Rapaport, and T. Sari, Le chemostat : Théorie mathématique de la culture continue de micro-organismes, 2016.

E. Harvey, J. Heys, and T. Gedeon, Quantifying the effects of the division of labor in metabolic pathways, Journal of Theoretical Biology, vol.360, issue.10, pp.222-242, 2014.
DOI : 10.1016/j.jtbi.2014.07.011

R. Kreikenbohm and E. Bohl, A mathematical model of syntrophic cocultures in the chemostat, FEMS Microbiology Letters, vol.110, issue.3, pp.131-140, 1986.
DOI : 10.1002/jctb.280350109

R. Kreikenbohm and E. Bohl, Bistability in the chemostat, Ecological Modelling, vol.43, issue.3-4, pp.287-301, 1988.
DOI : 10.1016/0304-3800(88)90009-9

J. Monod, LA TECHNIQUE DE CULTURE CONTINUE TH??ORIE ET APPLICATIONS, Ann. Inst. Pasteur, vol.79, issue.3, pp.390-410, 1950.
DOI : 10.1016/B978-0-12-460482-7.50023-3

B. J. Ni, G. P. Sheng, and H. Q. Yu, Model-based characterization of endogenous maintenance, cell death and predation processes of activated sludge in sequencing batch reactors, Chemical Engineering Science, vol.66, issue.4, pp.747-754, 2011.
DOI : 10.1016/j.ces.2010.11.033

A. Novick and L. Szilard, Description of the Chemostat, Science, vol.112, issue.2920, pp.715-716, 1950.
DOI : 10.1126/science.112.2920.715

I. Ramirez, E. I. Volcke, R. Rajinikanth, and J. P. Steyer, Modeling microbial diversity in anaerobic digestion through an extended ADM1 model, Water Research, vol.43, issue.11, pp.2787-2800, 2009.
DOI : 10.1016/j.watres.2009.03.034

P. J. Reilly, Stability of commensalistic systems, Biotechnology and Bioengineering, vol.32, issue.10, pp.1373-1392, 1974.
DOI : 10.1002/bit.260161006

T. Sari, M. Hajji, and J. Harmand, The mathematical analysis of a syntrophic relationship between two microbial species in a chemostat, Mathematical Biosciences and Engineering, vol.9, issue.3, pp.627-645, 2012.
DOI : 10.3934/mbe.2012.9.627
URL : https://hal.archives-ouvertes.fr/hal-00765311

T. Sari and J. Harmand, A model of a syntrophic relationship between two microbial species in a chemostat including maintenance, Mathematical Biosciences, vol.275, issue.97, pp.1-9, 2016.
DOI : 10.1016/j.mbs.2016.02.008
URL : https://hal.archives-ouvertes.fr/hal-01026149

T. Sari and M. J. Wade, Generalised approach to modelling a three-tiered microbial food-web, Mathematical Biosciences, vol.291, issue.9, pp.21-37, 2017.
DOI : 10.1016/j.mbs.2017.07.005
URL : https://hal.archives-ouvertes.fr/hal-01185634

M. Sbarciog, M. Loccufier, and E. Noldus, Determination of appropriate operating strategies for anaerobic digestion systems, Biochemical Engineering Journal, vol.51, issue.3, pp.180-188, 2010.
DOI : 10.1016/j.bej.2010.06.016

M. Sbarciog, A. Vande, and . Wouwer, Bifurcation analysis of an anaerobic digestion system, 2016 20th International Conference on System Theory, Control and Computing (ICSTCC), pp.330-335, 2016.
DOI : 10.1109/ICSTCC.2016.7790687

H. L. Smith and . Waltman, The Theory of the Chemostat, Dynamics of Microbial Competition, p.21, 1995.

G. Stephanopoulos, The dynamics of commensalism, Biotechnology and Bioengineering, vol.26, issue.10, pp.2243-2255, 1981.
DOI : 10.1002/bit.260231008

J. B. Van-lier, N. A. Mahmoud, and G. Zeeman, Anaerobic wastewater treatment Biological Wastewater Treatment : Principle, Modelling and Design, pp.415-456, 2008.

V. A. Vavilin, B. Fernandez, J. Palatsi, and X. Flotats, Hydrolysis kinetics in anaerobic degradation of particulate organic material : An overview ; Waste Management, pp.939-951, 2008.
DOI : 10.1016/j.wasman.2007.03.028

E. I. Volcke, M. Sbarciog, E. J. Noldus, B. De-baets, and M. Loccufier, Steady state multiplicity of two-step biological conversion systems with general kinetics, Mathematical Biosciences, vol.228, issue.2, pp.160-170, 2010.
DOI : 10.1016/j.mbs.2010.09.004
URL : https://biblio.ugent.be/publication/1045111/file/1245085.pdf

M. J. Wade, J. Harmand, B. Benyahia, T. Bouchez, S. Chaillou et al., Perspectives in mathematical modelling for microbial ecology, Ecological Modelling, vol.321, issue.10, pp.64-74, 2016.
DOI : 10.1016/j.ecolmodel.2015.11.002
URL : https://hal.archives-ouvertes.fr/hal-01227423

M. Weedermann and G. S. Wolkowicz, Optimal biogas production in a model for anaerobic digestion ; Nonlinear Dyn, pp.1097-1112, 2015.
DOI : 10.1007/s11071-015-2051-z

T. G. Wilkinson, H. H. Topiwala, and G. Hamer, Interactions in a mixed bacterial population growing on methane in continuous culture, Biotechnology and Bioengineering, vol.36, issue.1, pp.41-59, 1974.
DOI : 10.1111/j.1365-2672.1973.tb04107.x

A. Xu, J. Dolfing, T. P. Curtis, G. Montague, and E. Martin, Maintenance affects the stability of a two-tiered microbial ???food chain????, Journal of Theoretical Biology, vol.276, issue.1, pp.35-41, 2011.
DOI : 10.1016/j.jtbi.2011.01.026
URL : https://hal.archives-ouvertes.fr/hal-00682412

A. Yahmadi, Modèles mathématiques de relation syntrophique entre deux espèces microbiennes dans un chemostat ; Mastère : Modélisation mathématique et calcul scientifique, p.117, 2016.

@. Y. Daoud, N. Abdellatif, T. Sari, and J. Harmand, Steady state analysis of a syntrophic model : The effect of a new input substrate concentration, Mathematical modeling of natural phenomena, MMNP

@. Y. Daoud, N. Abdellatif, and J. Harmand, Modèles mathématiques de digestion anaérobie : effet de l'hydrolyse sur la production du biogaz Communications

@. Y. Daoud, N. Abdellatif, and J. Harmand, Analyse mathématique d'un modèle de digestion anaérobie avec phase d'hydrolyse Disponible sur https, 7ème colloque sur les Tendances des Applications en Mathématiques Tunisie Algérie Maroc

@. Y. Daoud, T. Sari, N. Abdellatif, and J. Harmand, Steady-state analysis of a syntrophic association of two species in a chemostat : The effect of a new input concentration substrate Disponible sur https, 4th International Conference on Complex Dynamical System in Life Sciences : Modeling and Analysis, 4thICCDS'2016, 2016.

@. Y. Daoud, N. Abdellatif, T. Sari, and J. Harmand, The effect of a new input concentration substrate on a syntrophic relationship of two species in a chemostat, 8ème colloque sur les Tendances des Applications en Mathématiques Tunisie Algérie Maroc
URL : https://hal.archives-ouvertes.fr/hal-01581516

. Mai-2017, Disponible sur https ://indico.math.cnrs.fr/event, pp.69-74, 1335.