Dans cette Note on propose une nouvelle fonction de Lyapunov pour l'étude de la stabilité asymptotique globale dans un modèle mathématique de compétition entre esspèces dans le chemostat. Le modèle inclut des fonctions de croissance monotones ou non monotones, des taux de mortalité différents pour chaque espèce et des taux de rendement variables, fonctions de la concentration en substrat. On obtient, comme corollaires de notre résultat, trois théorèmes de stabilité globale qui ont été considérés dans la litérature.
In this Note, we give a global asymptotic stability result for the competition mathematical model between several species in a chemostat, by using a new Lyapunov function. The model includes both monotone and non-monotone response functions, distinct removal rates for the species and variable yields, depending on the concentration of substrate. We obtain, as corollaries of our result, three global stability theorems which were considered in the literature.
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@article{CRMATH_2010__348_13-14_747_0, author = {Sari, Tewfik}, title = {A {Lyapunov} function for the chemostat with variable yields}, journal = {Comptes Rendus. Math\'ematique}, pages = {747--751}, publisher = {Elsevier}, volume = {348}, number = {13-14}, year = {2010}, doi = {10.1016/j.crma.2010.06.008}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2010.06.008/} }
TY - JOUR AU - Sari, Tewfik TI - A Lyapunov function for the chemostat with variable yields JO - Comptes Rendus. Mathématique PY - 2010 SP - 747 EP - 751 VL - 348 IS - 13-14 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2010.06.008/ DO - 10.1016/j.crma.2010.06.008 LA - en ID - CRMATH_2010__348_13-14_747_0 ER -
%0 Journal Article %A Sari, Tewfik %T A Lyapunov function for the chemostat with variable yields %J Comptes Rendus. Mathématique %D 2010 %P 747-751 %V 348 %N 13-14 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2010.06.008/ %R 10.1016/j.crma.2010.06.008 %G en %F CRMATH_2010__348_13-14_747_0
Sari, Tewfik. A Lyapunov function for the chemostat with variable yields. Comptes Rendus. Mathématique, Tome 348 (2010) no. 13-14, pp. 747-751. doi : 10.1016/j.crma.2010.06.008. http://archive.numdam.org/articles/10.1016/j.crma.2010.06.008/
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