Skip to Main content Skip to Navigation
Journal articles

Méthode d'agrégation des variables appliquée à la dynamique des populations

Abstract : We present the method of aggregation of variables in the case of ordinary differential equations. We apply the method to a prey - predator model in a multi - patchy environment. In this model, preys can go to a refuge and therefore escape to predation. The predator must return regularly to his terrier to feed his progeny. We study the effect of density-dependent migration on the global stability of the prey-predator system. We consider constant migration rates, but also density-dependent migration rates. We prove that the positif equilibrium is globally asymptotically stable in the first case, and that its stability changes in the second case. The fact that we consider density-dependent migration rates leads to the existence of a stable limit cycle via a Hopf bifurcation.
Document type :
Journal articles
Complete list of metadata

https://hal.inria.fr/hal-01263452
Contributor : Coordination Episciences Iam <>
Submitted on : Wednesday, January 27, 2016 - 5:15:33 PM
Last modification on : Wednesday, October 30, 2019 - 4:34:07 PM
Long-term archiving on: : Thursday, April 28, 2016 - 11:22:21 AM

File

arima00503.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : hal-01263452, version 1

Collections

Citation

Pierre Auger, Abderrahim El Abdllaoui, Rachid Mchich. Méthode d'agrégation des variables appliquée à la dynamique des populations. Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, INRIA, 2006, 5, pp.26-32. ⟨hal-01263452⟩

Share