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Convergence to equilibrium in competitive Lotka-Volterra and chemostat systems

Nicolas Champagnat 1, * Pierre-Emmanuel Jabin 1, 2 Gael Raoul 3
* Corresponding author
1 TOSCA
CNRS - Centre National de la Recherche Scientifique : UMR7502, INPL - Institut National Polytechnique de Lorraine, Université Nancy 2, UHP - Université Henri Poincaré - Nancy 1, CRISAM - Inria Sophia Antipolis - Méditerranée , INRIA Lorraine
Abstract : We study a generalized system of ODE's modeling a finite number of biological populations in a competitive interaction. We adapt the techniques in two previous articles to prove the convergence to a unique stable equilibrium.
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Nicolas Champagnat, Pierre-Emmanuel Jabin, Gael Raoul. Convergence to equilibrium in competitive Lotka-Volterra and chemostat systems. Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 2010, 348 (23-24), pp.1267-1272. ⟨10.1016/j.crma.2010.11.001⟩. ⟨inria-00495991⟩

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