Global asymptotic stability of coexistence steady-states in integro-differential Lotka-Volterra systems

Abstract : We analyse the asymptotic behaviour of integro-differential equations modelling N populations in interaction, where interactions are modelled by non-local terms involving linear combinations of the total number of individuals in each population. This model generalises the usual Lotka-Volterra ordinary differential equations. Our aim is to give conditions under which there is global asymptotical stability of coexistence steady-states at the level of the total number of individuals in each species. Through the analysis of a Lyapunov function, our first main result gives a simple and general condition on the matrix of interactions, together with a convergence rate. The second main result establishes another type of condition in the specific case of mutualistic interactions. These conditions are compared to the well-known condition given by Goh for classical Lotka-Volterra ordinary differential equations.
Type de document :
Pré-publication, Document de travail
2017
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01470722
Contributeur : Camille Pouchol <>
Soumis le : vendredi 17 février 2017 - 16:12:57
Dernière modification le : dimanche 26 mars 2017 - 01:07:08

Fichiers

ArticleLV_HAL_v1.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01470722, version 1
  • ARXIV : 1702.06187

Citation

Camille Pouchol, Emmanuel Trélat. Global asymptotic stability of coexistence steady-states in integro-differential Lotka-Volterra systems. 2017. <hal-01470722v1>

Partager

Métriques

Consultations de
la notice

411

Téléchargements du document

28