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

Convergence to equilibrium in competitive Lotka–Volterra and chemostat systems

Nicolas Champagnat, Pierre-Emmanuel Jabin, Gaël Raoul

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21 Scopus citations

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 Jabin and Raoul [8] and Champagnat and Jabin (2010) [2] to prove the convergence to a unique stable equilibrium. © 2010 Académie des sciences.

Original language	English (US)
Pages (from-to)	1267-1272
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	348
Issue number	23-24
DOIs	https://doi.org/10.1016/j.crma.2010.11.001
State	Published - Dec 2010
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-l1-007-43
Acknowledgements: The first author is grateful to Michel Benaim for useful discussions on the dynamical systems context of the problem. G.R. has been supported by Award No. KUK-l1-007-43 of Peter A. Markowich, made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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10.1016/j.crma.2010.11.001

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title = "Convergence to equilibrium in competitive Lotka–Volterra and chemostat systems",

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 Jabin and Raoul [8] and Champagnat and Jabin (2010) [2] to prove the convergence to a unique stable equilibrium. {\textcopyright} 2010 Acad{\'e}mie des sciences.",

author = "Nicolas Champagnat and Pierre-Emmanuel Jabin and Ga{\"e}l Raoul",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUK-l1-007-43 Acknowledgements: The first author is grateful to Michel Benaim for useful discussions on the dynamical systems context of the problem. G.R. has been supported by Award No. KUK-l1-007-43 of Peter A. Markowich, made by King Abdullah University of Science and Technology (KAUST). This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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AU - Champagnat, Nicolas

AU - Jabin, Pierre-Emmanuel

AU - Raoul, Gaël

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JF - Comptes Rendus Mathematique

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ER -

Convergence to equilibrium in competitive Lotka–Volterra and chemostat systems

Abstract

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