Some non-intuitive properties of simple extensions of the chemostat model

Ecological Complexity - Tập 34 - Trang 111-118 - 2018
Alain Rapaport1
1UMR 729 INRA/SupAgro MISTEA (Mathématiques, Informatique et STatistique pour l’Environnement et l’Agronomie), 2 pl. Viala, 34060 Montpellier, France

Tài liệu tham khảo

Amarasekare, 2001, Spatial heterogeneity, source sink dynamics, and the local coexistence of competing species, Am. Nat., 6, 572, 10.1086/323586 Andrews, 1968, A mathematical model for the continuous culture of microorganisms utilizing inhibitory substrates, Biotechnol. Bioeng., 10, 707, 10.1002/bit.260100602 Bastin, 1990 Butler, 1985, A mathematical model of the chemostat with a general class of functions describing nutrient uptake, SIAM J. Appl. Math., 45, 137, 10.1137/0145006 de Gooijer, 1996, Bioreactors in series: an overview of design procedures and practical applications, Enzyme Microb. Technol., 18, 202, 10.1016/0141-0229(95)00090-9 Dramé, 2006, Multiple steady state profiles in interconnected biological systems, Math. Comput. Model. Dyn. Syst., 12, 379, 10.1080/13873950600723277 Gaki, 2009, Complex dynamics of microbial competition in the gradostat, J. Biotechnol., 1, 38, 10.1016/j.jbiotec.2008.08.006 Gravel, 2010, Source and sink dynamics in metaecosystems, Ecology, 91, 2172, 10.1890/09-0843.1 Haidar, 2011, Effects of spatial structure and diffusion on the performances of the chemostat, Math. Biosci. Eng., 8, 953, 10.3934/mbe.2011.8.953 Haidar, 2011 Harmand, 1999, Optimal design of two interconnected bioreactors-some new results, Am. Inst. Chem. Eng. J., 49, 1433, 10.1002/aic.690490609 Hasler, 1954, The in situ chemostat – a self-contained continuous culturing and water sampling system, Limnol. Oceanogr., 79, 326 Higashi, 1998, In situ gradostat for the study of natural phytoplankton community with an experimental nutrient gradient, Environ. Pollut., 99, 395, 10.1016/S0269-7491(98)00026-8 Hill, 1989, Minimum tank volumes for CFST bioreactors in series, Can. J. Chem. Eng., 67, 818, 10.1002/cjce.5450670513 Hofbauer, 1994, Competition in the gradostat: the global stability problem, Nonlinear Anal.: Theory Methods Appl., 8, 1017, 10.1016/0362-546X(94)90064-7 Hsu, 1977, A mathematical theory for single-nutrient competition in continuous cultures of microorganisms, SIAM J. Appl. Math., 32, 366, 10.1137/0132030 Jaeger, 1987, Competition in the gradostat, J. Math. Biol., 25, 23, 10.1007/BF00275886 Koch, 1998 Lenas, 1998, Oscillations of two competing microbial populations in configurations of two interconnected chemostats, Math. Biosci., 1, 43, 10.1016/S0025-5564(97)10002-5 Li, 1998, Global asymptotic behavior of the chemostat: general response functions and differential removal rates, SIAM J. Appl. Math., 59, 411, 10.1137/S003613999631100X Lobry, 2017, The chemostat, mathematical theory of continuous culture of micro-organisms Lovitt, 1981, The gradostat: a bidirectional compound chemostat and its application in microbiological research, J. Gen. Microbiol., 127, 261 Luyben, 1982, Optimal design for continuously stirred tank reactors in series using Michaelis-Menten kinetics, Bioengineering, 24, 1217 Monod, 1950, La technique de culture continue: théorie et applications, Ann. Inst. Pasteur, Lille, 79, 390 Nakaoka, 2006, Competition in chemostat-type equations with two habitats, Math. Biosci., 201, 157, 10.1016/j.mbs.2005.12.011 Nelson, 2006, Evaluating the performance of a cascade of two bioreactors, Chem. Eng. Sci., 61, 3159, 10.1016/j.ces.2005.12.007 Novick, 1950, Experiments with the chemostat on spontaneous mutations of bacteria, Proc. Natl. Acad. Sci. U. S. A., 36, 708, 10.1073/pnas.36.12.708 Panikov, 1995 Pirt, 1975 Rapaport, 2008, Biological control of the chemostat with nonmonotonic response and different removal rates, Math. Biosci. Eng., 5, 539, 10.3934/mbe.2008.5.539 Rapaport, 2008, Coexistence in the design of a series of two chemostats, Nonlinear Anal.: Real World Appl., 9, 1052, 10.1016/j.nonrwa.2007.02.003 Rapaport, 2015, Global dynamics of the buffered chemostat for a general class of growth functions, J. Math. Biol., 71, 69, 10.1007/s00285-014-0814-7 Smith, 1989, Competition in the gradostat: the role of the communication rate, J. Math. Biol., 27, 139, 10.1007/BF00276100 Smith, 1991, The gradostat: a model of competition along a nutrient gradient, J. Microb. Ecol., 22, 207, 10.1007/BF02540224 Smith, 1995 Smith, 1991, Competition in an n-vessel gradostat, SIAM J. Appl. Math., 51, 1451, 10.1137/0151072 Stephanopoulos, 2006, Competition in chemostat-type equations with two habitats, Biotechnol. Bioeng., 21, 1491, 10.1002/bit.260210817 Tang, 1986, Mathematical investigations of growth of microorganisms in the gradostat, J. Math. Biol., 23, 319, 10.1007/BF00275252 Tang, 1994, Competition models in the gradostat with general nutrient uptake, Rocky Mountain J. Math., 24, 335 Veldcamp, 1977, Ecological studies with the chemostat, Adv. Microb. Ecol., 1, 59, 10.1007/978-1-4615-8219-9_2 Wolkowicz, 1992, Global dynamics of a mathematical model of competition in the chemostat: general response functions and differential death rates, SIAM J. Appl. Math., 52, 222, 10.1137/0152012