no. 23-24
Ordinary Differential Equations/Dynamical Systems
Convergence to equilibrium in competitive Lotka–Volterra and chemostat systems
[Convergence vers l'équilibre pour des systèmes compétitifs de Lotka–Volterra et du Chémostat]

Présenté par : Gérard Iooss

Champagnat, Nicolas1 ; Jabin, Pierre-Emmanuel1, 2 ; Raoul, Gaël3
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
Comptes Rendus. Mathématique, Tome 348 (2010) no. 23-24, pp. 1267-1272.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.11.001
Champagnat, Nicolas 1 ; Jabin, Pierre-Emmanuel 1, 2 ; Raoul, Gaël 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 
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     title = {Convergence to equilibrium in competitive {Lotka{\textendash}Volterra} and chemostat systems},
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Champagnat, Nicolas; Jabin, Pierre-Emmanuel; Raoul, Gaël. Convergence to equilibrium in competitive Lotka–Volterra and chemostat systems. Comptes Rendus. Mathématique, Tome 348 (2010) no. 23-24, pp. 1267-1272. doi : 10.1016/j.crma.2010.11.001. http://www.numdam.org/articles/10.1016/j.crma.2010.11.001/

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