M. Duffau, S. Aborhey, and D. Williamson, Modélisation d'un système proie-prédateur dans le cadre de la lutte biologique Application au couple A gossypii / H axyridis en serre de concombre State and parameter estimation of microbial growth processes, Automatica, vol.14, pp.493-498, 1978.

O. Arino and E. Sánchez, A Survey of Cell Population Dynamics, Journal of Theoretical Medicine, vol.1, issue.1, pp.35-51, 1997.
DOI : 10.1080/10273669708833005

S. Bains, R. Norris, R. Corfield, and K. Faul, Termination of global warmth at the palaeocene/eocene boundary through productivity feedback, Nature, vol.407, issue.6801, pp.171-174, 2000.
DOI : 10.1038/35025035

M. Ballyk and G. Wolkowicz, Exploitative competition in the chemostat for two perfectly substitutable resources, Mathematical Biosciences, vol.118, issue.2, pp.127-180, 1993.
DOI : 10.1016/0025-5564(93)90050-K

E. Beretta, P. Fergola, and C. Tenneriello, CHEMOSTAT EQUATIONS FOR A PREDATOR-PREY CHAIN WITH DELAYED NUTRIENT RECYCLING, Journal of Biological Systems, vol.03, issue.02, pp.483-494, 1995.
DOI : 10.1142/S0218339095000459

E. Beretta and Y. Takeuchi, QUALITATIVE PROPERTIES OF CHEMOSTAT EQUATIONS WITH TIME DELAYS, Differential Equations and Dynamical Systems, pp.19-40, 1994.
DOI : 10.1142/S0218339095000630

E. Beretta and Y. Takeuchi, Qualitative properties of chemostat equations with time delays II, Differential Equations and Dynamical Systems, pp.263-288, 1994.

A. Berman and R. Plemmons, Nonnegative matrices in the mathematical sciences, Classics in Applied Mathematics. SIAM, vol.9, 1994.
DOI : 10.1137/1.9781611971262

O. Bernard, Etude expérimentale et théorique de la croissance de Dunaliella tertiolecta (Chlorophyceae) soumisè a une limitation variable de nitrate. Utilisation de la dynamique transitoire pour la conception et la validation des modèles, 1995.

O. Bernard and J. Gouzé, Global qualitative behavior of a class of nonlinear biological systems; applications to the qualitative validation of phytoplankton growth models, 1998.

O. Bernard and J. Gouzé, Non-linear qualitative signal processing for biological systems: application to the algal growth in bioreactors, Mathematical Biosciences, vol.157, issue.1-2, pp.357-372, 1999.
DOI : 10.1016/S0025-5564(98)10091-3

O. Bernard, G. Malara, and A. Sciandra, The effects of a controlled fluctuating nutrient environment on continuous cultures of phytoplankton monitored by computers, Journal of Experimental Marine Biology and Ecology, vol.197, issue.2, pp.263-278, 1996.
DOI : 10.1016/0022-0981(95)00161-1

O. Bernard, G. Sallet, and A. Sciandra, Nonlinear observers for a class of biological systems: application to validation of a phytoplanktonic growth model, IEEE Transactions on Automatic Control, vol.43, issue.8, 1997.
DOI : 10.1109/9.704977

G. Butler, S. Hsu, and P. Waltman, A Mathematical Model of the Chemostat with Periodic Washout Rate, SIAM Journal on Applied Mathematics, vol.45, issue.3, pp.435-449, 1985.
DOI : 10.1137/0145025

G. Butler and G. Wolkowicz, A Mathematical Model of the Chemostat with a General Class of Functions Describing Nutrient Uptake, SIAM Journal on Applied Mathematics, vol.45, issue.1, pp.138-151, 1985.
DOI : 10.1137/0145006

M. Chappell and K. Godfrey, Structural identifiability of the parameters of a nonlinear batch reactor model, Mathematical Biosciences, vol.108, issue.2, pp.241-251, 1992.
DOI : 10.1016/0025-5564(92)90058-5

J. Cohen, Ergodic theorems in demography, Bulletin of the American Mathematical Society, vol.1, issue.2, pp.275-295, 1979.
DOI : 10.1090/S0273-0979-1979-14594-4

J. M. Cushing, A Competition Model for Size-Structured Species, SIAM Journal on Applied Mathematics, vol.49, issue.3, pp.838-858, 1989.
DOI : 10.1137/0149049

J. M. Cushing, An introduction to structured population dynamics, CBMS- NSF Regional Conference Series in Applied Mathematics. SIAM, Philadelphia, 1998.
DOI : 10.1137/1.9781611970005

H. El-owaidy and O. A. , Persistence in the chemostat, Mathematical Biosciences, vol.101, issue.1, pp.27-39, 1990.
DOI : 10.1016/0025-5564(90)90100-D

H. El-owaidy and O. A. , Theoretical studies on extinction in the gradostat, Mathematical Biosciences, vol.101, issue.1, pp.1-26, 1990.
DOI : 10.1016/0025-5564(90)90099-K

H. I. Freedman, J. W. So, and P. Waltman, Coexistence in a Model of Competition in the Chemostat Incorporating Discrete Delays, SIAM Journal on Applied Mathematics, vol.49, issue.3, pp.859-870, 1989.
DOI : 10.1137/0149050

Y. Fujimoto, H. Iwamoto, A. Kato, and K. Yamada, Studies on the growth rate of Chlorella by continuous cultivation, Bull. agric. chem. Soc. Japan, vol.20, pp.13-18, 1956.

E. Funasaki and M. Kot, Invasion and Chaos in a Periodically Pulsed Mass-Action Chemostat, Theoretical Population Biology, vol.44, issue.2, pp.203-224, 1993.
DOI : 10.1006/tpbi.1993.1026

T. B. Gage, F. M. Williams, and J. Horton, Division synchrony and the dynamics of microbial populations: A size-specific model, Theoretical Population Biology, vol.26, issue.3, pp.296-314, 1984.
DOI : 10.1016/0040-5809(84)90035-2

M. Golubitsky, E. B. Keeler, and M. Rothschild, Convergence of the age structure: Applications of the projective metric, Theoretical Population Biology, vol.7, issue.1, pp.84-93, 1975.
DOI : 10.1016/0040-5809(75)90007-6

A. Gragnani, O. De-feo, and S. Rinaldi, Food Chains in the Chemostat: Relationships Between Mean Yield and Complex Dynamics, Bulletin of Mathematical Biology, vol.60, issue.4, 1997.
DOI : 10.1006/bulm.1997.0039

J. Hale and A. S. Somolinos, Competition for fluctuating nutrient, Journal of Mathematical Biology, vol.11, issue.3, pp.255-280, 1983.
DOI : 10.1007/BF00276091

G. P. Harrison, Global stability of predator-prey interactions, Journal of Mathematical Biology, vol.18, issue.2, pp.159-171, 1979.
DOI : 10.1007/BF00279719

X. He and S. Ruan, Global stability in chemostat-type plankton models with delayed nutrient recycling, Journal of Mathematical Biology, vol.37, issue.3, 1996.
DOI : 10.1007/s002850050128

X. He, S. Ruan, and H. Xia, Global Stability in Chemostat-Type Equations with Distributed Delays, SIAM Journal on Mathematical Analysis, vol.29, issue.3, 1996.
DOI : 10.1137/S0036141096311101

X. He, S. Ruan, and H. Xia, Global Stability in Chemostat-Type Equations with Distributed Delays, SIAM Journal on Mathematical Analysis, vol.29, issue.3, pp.681-696, 1997.
DOI : 10.1137/S0036141096311101

J. Hofbauer and K. Sigmund, The theory of evolution and dynamical systems Mathematical aspects of selection, 1988.

R. Holmgren, A first course in discrete dynamical systems, 1996.

R. Horn and C. Johnson, Matrix analysis, 1990.

S. Hsu, A competition model for a seasonally fluctuating nutrient, Journal of Mathematical Biology, vol.7, issue.2, pp.115-132, 1980.
DOI : 10.1007/BF00275917

S. Hsu, K. Cheng, and S. P. Hubbell, Exploitative Competition of Microorganisms for Two Complementary Nutrients in Continuous Cultures, SIAM Journal on Applied Mathematics, vol.41, issue.3, pp.422-444, 1981.
DOI : 10.1137/0141036

S. Hsu, S. Hubbell, and P. Waltman, A Mathematical Theory for Single-Nutrient Competition in Continuous Cultures of Micro-Organisms, SIAM Journal on Applied Mathematics, vol.32, issue.2, pp.366-383, 1977.
DOI : 10.1137/0132030

S. B. Hsu and P. Waltman, Analysis of a Model of Two Competitors in a Chemostat with an External Inhibitor, SIAM Journal on Applied Mathematics, vol.52, issue.2, pp.528-540, 1991.
DOI : 10.1137/0152029

S. Hsu and P. Waltman, On a System of Reaction-Diffusion Equations Arising from Competition in an Unstirred Chemostat, SIAM Journal on Applied Mathematics, vol.53, issue.4, pp.1026-1044, 1993.
DOI : 10.1137/0153051

V. Hutson and K. Schmitt, Permanence and the dynamics of biological systems, Mathematical Biosciences, vol.111, issue.1, pp.1-71, 1992.
DOI : 10.1016/0025-5564(92)90078-B

S. Jang and L. Allen, A simple food chain with a growth inhibiting nutrient, Applied Mathematics and Computation, vol.104, issue.2-3, pp.277-298, 1999.
DOI : 10.1016/S0096-3003(98)10076-0

S. Jang and J. Baglama, Qualitative behavior of a variable-yield simple food chain with an inhibiting nutrient, Mathematical Biosciences, vol.164, issue.1, pp.65-80, 2000.
DOI : 10.1016/S0025-5564(99)00064-4

E. Keeler, A new method for ergodic analysis, 1974.

J. Keener, Oscillatory Coexistence in the Chemostat: A Codimension Two Unfolding, SIAM Journal on Applied Mathematics, vol.43, issue.5, pp.1005-1018, 1983.
DOI : 10.1137/0143066

M. Kimmel, Z. Darzynkiewicz, O. Arino, and F. Traganos, Analysis of a cell cycle model based on unequal division of metabolic constituents to daughter cells during cytokinesis, Journal of Theoretical Biology, vol.110, issue.4, pp.637-664, 1984.
DOI : 10.1016/S0022-5193(84)80149-6

B. Kooi, M. Boer, and S. Kooijman, Complex dynamic behaviour of autonomous microbial food chains, Journal of Mathematical Biology, vol.36, issue.1, pp.24-40, 1997.
DOI : 10.1007/s002850050088

B. Kooi, M. Boer, and S. Kooijman, Mass Balance Equation Versus Logistic Equation in Food Chains, Journal of Biological Systems, vol.05, issue.01, pp.77-85, 1997.
DOI : 10.1142/S0218339097000072

B. Kooi, M. Boer, and S. Kooijman, On the Use of the Logistic Equation in Models of Food Chains, Bulletin of Mathematical Biology, vol.60, issue.2, pp.231-246, 1998.
DOI : 10.1006/bulm.1997.0016

B. Kooi and S. Kooijman, Existence and Stability of Microbial Prey-Predator Systems, Journal of Theoretical Biology, vol.170, issue.1, pp.75-85, 1994.
DOI : 10.1006/jtbi.1994.1169

B. Kooi and S. Kooijman, The Transient Behaviour of Food Chains in Chemostats, Journal of Theoretical Biology, vol.170, issue.1, pp.87-94, 1994.
DOI : 10.1006/jtbi.1994.1170

B. Kooi and S. Kooijman, Many limiting behaviors in microbial food-chains, Mathematical Population Dynamics, Biological Systems, pp.131-148, 1995.

S. Kooijman, Dynamic Energy Budgets in biological systems. Theory and applications in ecotoxicology, 1993.

K. Lange and F. Oyarzun, The attractiveness of the droop equations, Mathematical Biosciences, vol.111, issue.2, pp.261-278, 1992.
DOI : 10.1016/0025-5564(92)90074-7

B. Li, Global Asymptotic Behavior of the Chemostat: General Response Functions and Different Removal Rates, SIAM Journal on Applied Mathematics, vol.59, issue.2, pp.411-422, 1999.
DOI : 10.1137/S003613999631100X

Z. Lu and K. Hadeler, Model of plasmid-bearing, plasmid-free competition in the chemostat with nutrient recycling and an inhibitor, Mathematical Biosciences, vol.148, issue.2, pp.147-159, 1998.
DOI : 10.1016/S0025-5564(97)10010-4

C. Maccluer, The Many Proofs and Applications of Perron's Theorem, SIAM Review, vol.42, issue.3, pp.487-498, 2000.
DOI : 10.1137/S0036144599359449

I. G. Minkevich, A. Yu, and . Abramychev, The dynamics of continuous microbial culture described by cell age distribution and concentration of one substrate, Bulletin of Mathematical Biology, vol.56, issue.5, pp.837-862, 1994.
DOI : 10.1016/S0092-8240(05)80293-9

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

J. Murray, Mathematical biology, 1989.

A. Novick and L. Szilard, Experiments with the Chemostat on Spontaneous Mutations of Bacteria, Proc. Nat. Acad. Sci, pp.708-719, 1950.
DOI : 10.1073/pnas.36.12.708

R. Nussbaum, Hilbert's projective metric and iterated nonlinear maps, Memoirs of the AMS, vol.75, issue.391, pp.1-137, 1988.

R. Nussbaum, Some Nonlinear Weak Ergodic Theorems, SIAM Journal on Mathematical Analysis, vol.21, issue.2, pp.436-460, 1990.
DOI : 10.1137/0521024

F. Oyarzun and K. Lange, The attractiveness of the droop equations II. generic uptake and growth functions, Mathematical Biosciences, vol.121, issue.2, pp.127-139, 1994.
DOI : 10.1016/0025-5564(94)90067-1

M. Pascual and H. Caswell, From the cell cycle to population cycles in phytoplanktonnutrient interactions, Ecology, vol.78, issue.3, pp.897-912, 1997.

Q. Peng and H. Freedman, Global Attractivity in a Periodic Chemostat with General Uptake Functions, Journal of Mathematical Analysis and Applications, vol.249, issue.2, pp.300-323, 2000.
DOI : 10.1006/jmaa.2000.6757

S. Pilyugin and P. Waltman, Competition in the unstirred chemostat with periodic input and washout, SIAM J. Appl. Math, vol.59, issue.4, pp.1157-1177, 1999.

S. Pilyugin and P. Waltman, The Simple Chemostat with Wall Growth, SIAM Journal on Applied Mathematics, vol.59, issue.5, pp.1552-1572, 1999.
DOI : 10.1137/S0036139997326181

N. Rao and E. Roxin, Controlled Growth of Competing Species, SIAM Journal on Applied Mathematics, vol.50, issue.3, pp.853-864, 1990.
DOI : 10.1137/0150049

S. Ruan and X. He, Global stability in chemostat-type competition models with nutrient recycling, 1996.

S. Ruan and X. He, Global Stability in Chemostat-Type Competition Models with Nutrient Recycling, SIAM Journal on Applied Mathematics, vol.58, issue.1, pp.170-192, 1998.
DOI : 10.1137/S0036139996299248

E. Seneta, Non-negative matrices and Markov chains. Springer Series in Statistics, 1981.

H. L. Smith, Competitive Coexistence in an Oscillating Chemostat, SIAM Journal on Applied Mathematics, vol.40, issue.3, pp.498-522, 1981.
DOI : 10.1137/0140042

H. L. Smith, Monotone dynamical systems, 1995.
DOI : 10.1090/surv/041/01

H. L. Smith, A discrete, size-structured model of microbial growth and competition in the chemostat, Journal of Mathematical Biology, vol.36, issue.7, pp.734-754, 1996.
DOI : 10.1007/BF00161517

H. L. Smith, The periodically forced Droop model for phytoplankton growth in a chemostat, Journal of Mathematical Biology, vol.35, issue.5, pp.545-556, 1997.
DOI : 10.1007/s002850050065

H. L. Smith, P. Tang, and . Waltman, -Vessel Gradostat, SIAM Journal on Applied Mathematics, vol.51, issue.5, pp.1451-1471, 1991.
DOI : 10.1137/0151072

URL : https://hal.archives-ouvertes.fr/hal-00309731

H. L. Smith and P. Waltman, Competition for a Single Limiting Resource in Continuous Culture: The Variable-Yield Model, SIAM Journal on Applied Mathematics, vol.54, issue.4, pp.1113-1131, 1994.
DOI : 10.1137/S0036139993245344

H. L. Smith and P. Waltman, The theory of the chemostat. Dynamics of microbial competition, Cambridge Studies in Mathematical Biology, vol.13, 1995.

G. Stephanopoulos, A. Fredrickson, and R. Aris, The growth of competing microbial populations in a CSTR with periodically varying inputs, AIChE Journal, vol.25, issue.5, pp.863-872, 1979.
DOI : 10.1002/aic.690250515

N. Thomopoulos, D. Vayenas, and S. Pavlou, On the coexistence of three microbial populations competing for two complementary substrates in configurations of interconnected chemostats, Mathematical Biosciences, vol.154, issue.2, pp.87-102, 1998.
DOI : 10.1016/S0025-5564(98)10047-0

S. Tuljapurkar and H. Caswell, Structured-population models in marine, terrestrial , and freshwater systems, volume 18 of Population and community biology series, 1996.

D. Vayenas and S. Pavlou, Chaotic dynamics of a food web in a chemostat, Mathematical Biosciences, vol.162, issue.1-2, pp.69-84, 1999.
DOI : 10.1016/S0025-5564(99)00044-9

D. Vayenas and S. Pavlou, Coexistence of three microbial populations competing for three complementary nutrients in a chemostat, Mathematical Biosciences, vol.161, issue.1-2, pp.1-13, 1999.
DOI : 10.1016/S0025-5564(99)00040-1

F. M. Williams, A model of cell growth dynamics, Journal of Theoretical Biology, vol.15, issue.2, pp.190-207, 1967.
DOI : 10.1016/0022-5193(67)90200-7

F. M. Williams, Dynamics of Microbial Populations, Systems Analysis and Simulation in Ecology, pp.198-267, 1971.
DOI : 10.1016/B978-0-12-547201-2.50011-X

G. Wolkowicz, Successful invasion of a food web in a chemostat, Mathematical Biosciences, vol.93, issue.2, pp.249-268, 1989.
DOI : 10.1016/0025-5564(89)90025-4

G. Wolkowicz and Z. Lu, Global Dynamics of a Mathematical Model of Competition in the Chemostat: General Response Functions and Differential Death Rates, SIAM Journal on Applied Mathematics, vol.52, issue.1, pp.222-233, 1992.
DOI : 10.1137/0152012

G. Wolkowicz and H. Xia, Global Asymptotic Behavior of a Chemostat Model with Discrete Delays, SIAM Journal on Applied Mathematics, vol.57, issue.4, pp.1019-1043, 1997.
DOI : 10.1137/S0036139995287314

G. Wolkowicz, H. Xia, and S. Ruan, Competition in the Chemostat: A Distributed Delay Model and Its Global Asymptotic Behavior, SIAM Journal on Applied Mathematics, vol.57, issue.5, pp.1281-1310, 1997.
DOI : 10.1137/S0036139995289842

G. S. Wolkowicz and X. Zhao, n-species competition in a periodic chemostat, Differential Integral Equations, vol.11, issue.3, pp.465-491, 1998.

J. Wu, Global bifurcation of coexistence state for the competition model in the chemostat, Nonlinear Analysis: Theory, Methods & Applications, vol.39, issue.7, pp.817-835, 2000.
DOI : 10.1016/S0362-546X(98)00250-8