Convergence to equilibrium in competitive Lotka–Volterra and chemostat systems

Nicolas Champagnat; Pierre-Emmanuel Jabin; Gaël Raoul

doi:10.1016/j.crma.2010.11.001

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

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

Comptes Rendus. Mathématique, Volume 348 (2010) no. 23-24, pp. 1267-1272.

Résumé
Abstract

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 : 2010-07-06
Accepté le : 2010-10-05
Publié le : 2010-11-17

DOI : 10.1016/j.crma.2010.11.001

Affiliations des auteurs :

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

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     title = {Convergence to equilibrium in competitive {Lotka{\textendash}Volterra} and chemostat systems},
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     doi = {10.1016/j.crma.2010.11.001},
     language = {en},
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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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.11.001/

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