Qualitative stability patterns for Lotka-Volterra systems on rectangles

Laurent Tournier 1, * Jean-Luc Gouzé 1
* Auteur correspondant
1 COMORE - Modeling and control of renewable resources
LOV - Laboratoire d'océanographie de Villefranche, CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We present a qualitative analysis of the Lotka-Volterra differential equation within rectangles that are transverse with respect to the flow. In similar way to existing works on affine systems (and positively invariant rectangles), we consider here nonlinear Lotka-Volterra n-dimensional equation, in rectangles with any kind of tranverse patterns. We give necessary and sufficient conditions for the existence of symmetrically transverse rectangles (containing the positive equilibrium), giving notably the method to build such rectangles. We also analyse the stability of the equilibrium thanks to this transverse pattern. We finally propose an analysis of the dynamical behavior inside a rectangle containing the positive equilibrium, based on Lyapunov stability theory. More particularly, we make use of Lyapunov-like functions, built upon vector norms. This work is a first step towards a qualitative abstraction and simulation of Lotka-Volterra systems.
Type de document :
[Research Report] RR-6346, INRIA. 2007, pp.16
Liste complète des métadonnées

Littérature citée [17 références]  Voir  Masquer  Télécharger

Contributeur : Rapport de Recherche Inria <>
Soumis le : jeudi 8 novembre 2007 - 15:54:11
Dernière modification le : mercredi 19 septembre 2018 - 01:21:36
Document(s) archivé(s) le : mardi 21 septembre 2010 - 15:10:44


Fichiers produits par l'(les) auteur(s)


  • HAL Id : inria-00186247, version 2



Laurent Tournier, Jean-Luc Gouzé. Qualitative stability patterns for Lotka-Volterra systems on rectangles. [Research Report] RR-6346, INRIA. 2007, pp.16. 〈inria-00186247v2〉



Consultations de la notice


Téléchargements de fichiers