Comptes Rendus
Ordinary Differential Equations/Dynamical Systems
Convergence to equilibrium in competitive Lotka–Volterra and chemostat systems
Comptes Rendus. Mathématique, Volume 348 (2010) no. 23-24, pp. 1267-1272.

We study a generalized system of ODE's modeling a finite number of biological populations in a competitive interaction. We adapt the techniques in Jabin and Raoul [8] and Champagnat and Jabin (2010) [2] to prove the convergence to a unique stable equilibrium.

Nous étudions un système généralisé d'équations différentielles modélisant un nombre fini de populations biologiques en interaction compétitive. En adaptant les techniques de Jabin et Raoul [8] et de Champagnat et Jabin (2010) [2], nous prouvons la convergence vers un unique équilibre stable.

Published online:
DOI: 10.1016/j.crma.2010.11.001

Nicolas Champagnat 1; Pierre-Emmanuel Jabin 1, 2; Gaël Raoul 3

1 TOSCA project-team, INRIA Sophia Antipolis – Méditerranée, 2004 rte des Lucioles, B.P. 93, 06902 Sophia Antipolis Cedex, France
2 Laboratoire J.-A. Dieudonné, Université de Nice – Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 02, France
3 DAMTP, CMS, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
     author = {Nicolas Champagnat and Pierre-Emmanuel Jabin and Ga\"el Raoul},
     title = {Convergence to equilibrium in competitive {Lotka{\textendash}Volterra} and chemostat systems},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1267--1272},
     publisher = {Elsevier},
     volume = {348},
     number = {23-24},
     year = {2010},
     doi = {10.1016/j.crma.2010.11.001},
     language = {en},
AU  - Nicolas Champagnat
AU  - Pierre-Emmanuel Jabin
AU  - Gaël Raoul
TI  - Convergence to equilibrium in competitive Lotka–Volterra and chemostat systems
JO  - Comptes Rendus. Mathématique
PY  - 2010
SP  - 1267
EP  - 1272
VL  - 348
IS  - 23-24
PB  - Elsevier
DO  - 10.1016/j.crma.2010.11.001
LA  - en
ID  - CRMATH_2010__348_23-24_1267_0
ER  - 
%0 Journal Article
%A Nicolas Champagnat
%A Pierre-Emmanuel Jabin
%A Gaël Raoul
%T Convergence to equilibrium in competitive Lotka–Volterra and chemostat systems
%J Comptes Rendus. Mathématique
%D 2010
%P 1267-1272
%V 348
%N 23-24
%I Elsevier
%R 10.1016/j.crma.2010.11.001
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%F CRMATH_2010__348_23-24_1267_0
Nicolas Champagnat; Pierre-Emmanuel Jabin; Gaël Raoul. Convergence to equilibrium in competitive Lotka–Volterra and chemostat systems. Comptes Rendus. Mathématique, Volume 348 (2010) no. 23-24, pp. 1267-1272. doi : 10.1016/j.crma.2010.11.001.

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[11] B. Perthame Transport Equations in Biology, Frontiers in Mathematics, Birkhäuser, 2007

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