Claude Lobry ; Tewfik Sari - Migrations in the Rosenzweig-MacArthur model and the "atto-fox" problem

arima:1990 - Revue Africaine de Recherche en Informatique et Mathématiques Appliquées, November 8, 2015, Volume 20 - 2015 - Special issue - Colloquium in Honor of Éric Benoît - https://doi.org/10.46298/arima.1990
Migrations in the Rosenzweig-MacArthur model and the "atto-fox" problemArticle

Authors: Claude Lobry 1,2; Tewfik Sari ORCID3,4,5

  • 1 Université Nice Sophia Antipolis (1965 - 2019)
  • 2 Modelling and Optimisation of the Dynamics of Ecosystems with MICro-organisme
  • 3 Laboratoire de Mathématiques Informatique et Applications
  • 4 Information – Technologies – Analyse Environnementale – Procédés Agricoles
  • 5 Laboratoire de Mathématiques Informatique et Applications [UHA]

The Rosenzweig-MacArthur model is a system of two ODEs used in population dynamics to modelize the predator-prey relationship. For certain values of the parameters the differential system exhibits a unique stable limit cycle. When the dynamics of the prey is faster than the dynamics of the predator, during oscillations along the limit cycle, the density of preys take so small values that it cannot modelize any actual population. This phenomenon is known as the "atto-fox" problem. In this paper we assume that the populations are living in two patches and are able to migrate from one patch to another. We give conditions for which the migration can prevent the density of prey being too small.


Volume: Volume 20 - 2015 - Special issue - Colloquium in Honor of Éric Benoît
Published on: November 8, 2015
Submitted on: April 12, 2015
Keywords: Rosenzweig-MacArthur model, "atto-fox" problem, singular perturbations, limit cycles, nonstandard analysis,Modèle de Rosenzweig-MacArthur, migration, problème "atto-fox", perturbations singulières, cycles limites, analyse non standard, canards,[INFO] Computer Science [cs],[MATH] Mathematics [math]

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