Pierre Auger ; Abderrahim El Abdllaoui ; Rachid Mchich - Méthode d'agrégation des variables appliquée à la dynamique des populations

arima:1852 - Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, October 4, 2006, Volume 5, Special Issue TAM TAM'05, november 2006 - https://doi.org/10.46298/arima.1852
Méthode d'agrégation des variables appliquée à la dynamique des populations

Authors: Pierre Auger ; Abderrahim El Abdllaoui ; Rachid Mchich

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.


Volume: Volume 5, Special Issue TAM TAM'05, november 2006
Published on: October 4, 2006
Submitted on: March 17, 2006
Keywords: Aggregation of variables, time scales, population dynamics, prey-predator,Agrégation des variables,éhelles de temps,dynamique de population,proie-prédateur,[MATH] Mathematics [math],[INFO] Computer Science [cs]


Share

Consultation statistics

This page has been seen 173 times.
This article's PDF has been downloaded 83 times.