no. 3
Ordinary Differential Equations/Automation (theoretical)
Persistence in ecological models of competition for a single resource
[Persistance dans les modèles écologiques de compétition pour une seule ressource.]

Présenté par : Pierre-Louis Lions

Lobry, Claude1 ; Mazenc, Frédéric1 ; Rapaport, Alain1
1 Projet INRA-INRIA ‘MERE’, UMR analyse des systèmes et biométrie, 2, place Viala, 34060 Montpellier, France
Comptes Rendus. Mathématique, Tome 340 (2005) no. 3, pp. 199-204.

Nous montrons comment la considération d'un terme de compétition intra-specifique dans les lois de croissance permet d'expliquer la persistance stable de plusieurs espèces en compétition pour une même ressource. Ce résultat est appliqué à un modèle de compétition pour un seul substrat dans le chemostat.

We show how the consideration of an intra-specific dependency in the population growth functions can explain a stable persistence of several species in competition for a single resource. This result is applied to a model of single-nutrient competition in the chemostat.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2004.12.021
Lobry, Claude 1 ; Mazenc, Frédéric 1 ; Rapaport, Alain 1

1 Projet INRA-INRIA ‘MERE’, UMR analyse des systèmes et biométrie, 2, place Viala, 34060 Montpellier, France 
@article{CRMATH_2005__340_3_199_0,
     author = {Lobry, Claude and Mazenc, Fr\'ed\'eric and Rapaport, Alain},
     title = {Persistence in ecological models of competition for a single resource},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {199--204},
     publisher = {Elsevier},
     volume = {340},
     number = {3},
     year = {2005},
     doi = {10.1016/j.crma.2004.12.021},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2004.12.021/}
}
TY  - JOUR
AU  - Lobry, Claude
AU  - Mazenc, Frédéric
AU  - Rapaport, Alain
TI  - Persistence in ecological models of competition for a single resource
JO  - Comptes Rendus. Mathématique
PY  - 2005
SP  - 199
EP  - 204
VL  - 340
IS  - 3
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2004.12.021/
DO  - 10.1016/j.crma.2004.12.021
LA  - en
ID  - CRMATH_2005__340_3_199_0
ER  - 
%0 Journal Article
%A Lobry, Claude
%A Mazenc, Frédéric
%A Rapaport, Alain
%T Persistence in ecological models of competition for a single resource
%J Comptes Rendus. Mathématique
%D 2005
%P 199-204
%V 340
%N 3
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2004.12.021/
%R 10.1016/j.crma.2004.12.021
%G en
%F CRMATH_2005__340_3_199_0
Lobry, Claude; Mazenc, Frédéric; Rapaport, Alain. Persistence in ecological models of competition for a single resource. Comptes Rendus. Mathématique, Tome 340 (2005) no. 3, pp. 199-204. doi : 10.1016/j.crma.2004.12.021. http://www.numdam.org/articles/10.1016/j.crma.2004.12.021/

[1] Angeli, D.; Sontag, E. Monotone Control Systems, IEEE Trans. Automat. Control, Volume 48 (2003), pp. 1684-1698

[2] Angeli, D.; Sontag, E. Optimal Control, Stabilization and Nonsmooth Analysis (de Queiroz, M.S.; Malisoff, M.; Wolenski, P., eds.), Lecture Notes in Control and Inform. Sci., Springer, 2004, pp. 135-154

[3] Butler, G.J.; Hsu, S.B.; Waltman, P. A mathematical model of the chemostat with periodic washout rate, SIAM J. Appl. Math., Volume 45 (1985), pp. 435-449

[4] De Leenheer, P.; Angeli, D.; Sontag, E.D. A feedback perspective for chemostat models with crowding effects, Lecture Notes in Control and Inform. Sci., vol. 294, 2003, pp. 167-174

[5] De Leenheer, P.; Smith, H.L. Feedback control for the chemostat, J. Math. Biol., Volume 46 (2003), pp. 48-70

[6] F. Grognard, F. Mazenc, A. Rapaport, 2005, in preparation

[7] Grover, J.P. Resource Competition, Chapman & Hall, New York, 1997

[8] Hale, J.K.; Somolinas, A.S. Competition for fluctuating nutrient, J. Math. Biol., Volume 18 (1983), pp. 255-280

[9] Hansen, S.; Hubbell, S. Single-nutrient microbial competition: qualitative agreement between experimental and theoretically forecast outcomes, Science, Volume 207 (1980) no. 28, pp. 1491-1493

[10] Hardin, G. The competition exclusion principle, Science, Volume 131 (1960), pp. 1292-1298

[11] Hsu, S.B. A competition model for a seasonally fluctuating nutrient, J. Math. Biol., Volume 9 (1980), pp. 115-132

[12] Hsu, S.B.; Cheng, K.S.; Hubbell, S.P. Exploitative competition of micro-organisms for two complementary nutrients in continuous culture, SIAM J. Appl. Math., Volume 41 (1981), pp. 422-444

[13] Leon, J.A.; Tumpson, D.B. Competition between two species for two complementary or substituable resources, J. Theor. Biol., Volume 50 (1975), pp. 185-201

[14] C. Lobry, R. Arditi, J. Harmand, J.J. Godon, A. Sciandra, 2005, in preparation

[15] Lobry, C.; Sari, T.; Touhami, S. Slow and fast feed back in control systems, J. Biol. Syst., Volume 7 (1999) no. 3, pp. 307-332

[16] Metz, J.; Dieckmann, O. The Dynamics of Physilogically Structured Populations, Lecture Notes in Biomath., vol. 68, Springer, Berlin Germany, 1986

[17] Panikov, N.S. Microbial Growth Kinetics, Chapman and Hall, New York, 1995

[18] Smith, H.L.; Waltman, P. The Theory of the Chemostat, Cambridge University Press, 1995

[19] Stephanopoulos, G.; Fredrickson, A.G.; Aris, R. The growth of competing microbial populations in CSTR with periodically varying inputs, Amer. Inst. Chem. Engrg. J., Volume 25 (1979), pp. 863-872

Cité par Sources :