How flocculation can explain coexistence in the chemostat

Journal of Biological Dynamics

Volumn 2, Issue 1, 2008, Pages 1-13

  Haegeman, B ^a   Rapaport, A ^b  

^a LABORATOIRE DE BIOTECHNOLOGIE DE L ENVIRONNEMENT   (France)

^b UMR Analyse des Systèmes et Biométrie 2 place Pierre Viala ^*  (France)

Author keywords

Chemostat; Competition; Density dependence; Flocculation; Persistence

Indexed keywords

ARTICLE; BIOLOGICAL MODEL; BIOREACTOR; COMPUTER SIMULATION; FLOCCULATION; MICROBIOLOGY;

BIOREACTORS; COMPUTER SIMULATION; FLOCCULATION; MODELS, BIOLOGICAL;

EID: 52049110860     PISSN: 17513758     EISSN: 17513766     Source Type: Journal    
DOI: 10.1080/17513750801942537     Document Type: Article

References (24)

1. Auger, P., and Benoît, E., 1993. A prey-predator model in a multi-patch environment with different time scales. J. Biol. Syst., 1:187–197.
2. Auger, P., and Poggiale, J.-C., 1996. Emergence of population growth models:Fast migration and slow growth. J. Theor. Biol., 182:99–108.
3. Butler, G. J., Hsu, S. B., and Waltman, P., 1985. A mathematical model of the chemostat with periodic washout rate. SIAM J. Appl. Math., 45:435–449.
4. Chiu, Z. C., 2007. Oxygen diffusion and consumption in active aerobic granules of heterogeneous structure. Appl. Microbiol. Biotechnol., 75:685–691.
5. De Leenheer, P., Angeli, D., and Sontag, E. D., 2003. A feedback perspective for chemostat models with crowding effects. Lecture Notes Contr. Inf. Sci., 294:167–174.
6. Dhooge, A., Govaerts, W., and Kuznetsov, Y. A., 2003. MATCONT:A MATLAB package for numerical bifurcation analysis of ODEs. ACM Trans. Math. Soft., 29:141–164.
7. Ginovart, M., 2006. Flocculation in brewing yeasts:A computer simulation study. BioSystems, 83:51–55.
8. Haegeman, B., Lobry, C., and Harmand, J., 2007. Modeling bacteria flocculation as density-dependent growth. AIChE J., 53:535–539.
9. Hale, J. K., and Somolinas, A. S., 1983. Competition for fluctuating nutrient. J. Math. Biol., 18:255–280.
10. Hansen, S., and Hubbell, S., 1980. Single-nutrient microbial competition:Qualitative agreement between experimental and theoretically forecast outcomes. Science, 207:1491–1493.
11. Hardin, G., 1960. The competition exclusion principle. Science, 131:1292–1298.
12. Hutchinson, G. E., 1961. The paradox of the plankton. Am. Nat., 95:137–145.
13. Khalil, H. K., 1996. Nonlinear Systems, 2, New Jersey, USA:Prentice Hall.
14. Li, B., and Bishop, L., 2004. Micro-profiles of activated sludge floc determined using microelectrodes. Water Res., 38:1248–1258.
15. Lobry, C., Mazenc, F., and Rapaport, A., 2005. Persistence in ecological models of competition for a single resource. C.R. Acad. Sci. Paris, Math., 340:199–204.
16. Martins, A. P., 2004. Three-dimensional dual-morphotype species modeling of activated sludge flocs. Environ. Sci. Technol., 38:5632–5641.
17. Monod, J., 1942. Recherches sur la Croissance des Cultures Bactériennes, Paris, France:Hermann.
18. Poggiale, J. C., Michalski, J., and Arditi, R., 1998. Emergence of donor control in patchy predator-prey systems. Bull. Math. Biol., 60:1149–1166.
19. Sari, T., 2005. Contrôle Non Linéaire et Applications, Paris, France:Hermann. Lecture notes of the CIMPA summer school, University of Tlemcen
20. Smith, H. L., 1995. Monotone Dynamical Systems. An introduction to the Theory of Competitve and Cooperative Systems, Vol. 7, American Mathematical Society. Mathematical Surveys And Monographs
21. Smith, H., and Waltman, P., 1985. The Theory of the Chemostat:Dynamics of Microbial Competition, Cambridge Studies in Mathematical Biology, Cambridge University Press.
22. Stephanopoulos, G., and Fredrickson, A. G., 1979. Effect of spatial inhomogeneneities on the coexistence of competing microbial populations. Biotech. Bioeng., 21:1491–1498.
23. Thieme, H. R., 1994. Asymptotically autonomous differential equations in the plane. II. Stricter Poincaré/Bendixson type results. Diff. Int. Eq., 7:1625–1640.
24. Thomas, D. N., Judd, S. J., and Fawcett, N., 1999. Flocculation modelling:A review. Water Res., 33:1579–1592.