R. A. Armstrong and R. Mcgehee, Competitive exclusion, The American Naturalist, vol.115, issue.2, pp.151-170, 1980.

M. Benaïm, S. L. Borgne, F. Malrieu, and P. Zitt, On the stability of planar randomly switched systems, Ann. Appl. Probab, vol.24, issue.1, pp.292-311, 2014.

M. Benaïm and C. Lobry, Lotka-Volterra with randomly fluctuating environments or "How switching between beneficial environments can make survival harder, Ann. Appl. Probab, vol.26, issue.6, pp.3754-3785, 2016.

A. Berman and R. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Society for Industrial and Applied Mathematics, 1994.

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.

F. Campillo, M. Joannides, and I. Larramendy-valverde, Stochastic modeling of the chemostat, Ecological Modelling, vol.222, issue.15, pp.2676-2689, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00641231

F. Castella and S. Madec, Coexistence phenomena and global bifurcation structure in a chemostatlike model with species-dependent diffusion rates, Journal of Mathematical Biology, vol.68, issue.1, pp.377-415, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00777025

F. Castella, S. Madec, and Y. Lagadeuc, Global behavior of N competing species with strong diffusion: diffusion leads to exclusion, Applicable Analysis, vol.95, issue.2, pp.341-372, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01026195

P. Chesson, Mechanisms of Maintenance of Species Diversity, Annual Review of Ecology and Systematics, vol.31, issue.1, pp.343-366, 2000.

P. L. Chesson and R. R. Warner, Environmental Variability Promotes Coexistence in Lottery Competitive Systems, The American Naturalist, vol.117, issue.6, pp.923-943, 1981.

C. T. Codeço, J. P. Grover, and A. E. Deangelis, Competition along a spatial gradient of resource supply: A microbial experimental model, The American Naturalist, vol.157, issue.3, pp.300-315, 2001.

M. H. Davis, Piecewise-deterministic Markov processes: a general class of nondiffusion stochastic models, J. Roy. Statist. Soc. Ser. B, vol.46, issue.3, pp.353-388, 1984.

A. Gaki, A. Theodorou, D. V. Vayenas, and S. Pavlou, Complex dynamics of microbial competition in the gradostat, Journal of Biotechnology, vol.139, issue.1, pp.38-46, 2009.

B. Haegeman and A. Rapaport, How flocculation can explain coexistence in the chemostat, Journal of Biological Dynamics, vol.2, issue.1, p.22876841, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00857826

S. Hansen and S. Hubbell, Single-nutrient microbial competition: qualitative agreement between experimental and theoretically forecast outcomes, Science, vol.207, issue.4438, pp.1491-1493, 1980.

J. Hofbauer, J. , and W. So, Competition in the gradostat: the global stability problem, Nonlinear Analysis: Theory, Methods & Applications, vol.22, pp.1017-1031, 1994.

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.

S. B. Hsu, Limiting behavior for competing species, SIAM J. Appl. Math, vol.34, issue.4, pp.760-763, 1978.

S. B. Hsu, S. Hubbell, and P. Waltman, A mathematical theory for single-nutrient competition in continuous cultures of micro-organisms, SIAM J. Appl. Math, vol.32, issue.2, pp.366-383, 1977.

G. E. Hutchinson, The paradox of the plankton, The American Naturalist, vol.95, issue.882, pp.137-145, 1961.

W. Jäger, J. W. So, B. Tang, and P. Waltman, Competition in the gradostat, Journal of Mathematical Biology, 1987.

G. Lagasquie, Etude du Comportement en temps long de processus de markov deterministes par morceaux, vol.7, 2018.

P. Lenas and S. Pavlou, Periodic, quasi-periodic, and chaotic coexistence of two competing microbial populations in a periodically operated chemostat, Mathematical Biosciences, vol.121, issue.1, pp.61-110, 1994.

M. Loreau, N. Mouquet, and A. Gonzalez, Biodiversity as spatial insurance in heterogeneous landscapes, Proceedings of the National Academy of Sciences, vol.100, issue.22, pp.12765-12770, 2003.

R. Lovitt and J. Wimpenny, The gradostat: a bidirectional compound chemostat and its application in microbiological research, J Gen Microbiol, 1981.

F. Malrieu and P. Zitt, On the persistence regime for lotka-volterra in randomly fluctuating environments, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01264637

D. M. , Some thoughts on nutrient limitation in algae, Journal of Phycology, vol.9, issue.3, pp.264-272, 1973.

A. Rapaport, Some non-intuitive properties of simple extensions of the chemostat model, Ecological Complexity, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01465572

A. Rapaport and I. Haidar, Effects of spatial structure and diffusion on the performances of the chemostat, Mathematical Biosciences and Engineering, vol.8, issue.4, pp.953-971, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01001373

S. Roy and J. Chattopadhyay, Towards a resolution of 'the paradox of the plankton': A brief overview of the proposed mechanisms, Ecological Complexity, vol.4, issue.1, pp.26-33, 2007.

H. Smith and P. Waltman, The gradostat: A model of competition along a nutrient gradient, Microbial Ecology, vol.22, issue.1, pp.207-226, 1991.

H. Smith and P. Waltman, The Theory of the Chemostat Dynamics of Microbial Competition, 1995.

H. Smith and P. Waltman, Competition in the periodic gradostat, Nonlinear Analysis: Real World Applications, vol.1, issue.1, pp.177-188, 2000.

H. L. Smith, B. Tang, and P. Waltman, Competition in an n-vessel gradostat, SIAM Journal on Applied Mathematics, vol.51, issue.5, pp.1451-1471, 1991.

E. Strickler and M. Benaim, Random switching between vector fields having a common zero, 2017.

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

L. Wang and D. Jiang, Ergodic property of the chemostat: A stochastic model under regime switching and with general response function, Nonlinear Analysis: Hybrid Systems, vol.27, pp.341-352, 2018.

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.