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Dynamic transcritical bifurcations in a class of slow-fast predator-prey models

Hafida Boudjellaba 1 Tewfik Sari 2, 3
1 Department of Mathematics and Computer Science [Laurentian Univ.]
2 MERE - Water Resource Modeling
CRISAM - Inria Sophia Antipolis - Méditerranée , INRA - Institut National de la Recherche Agronomique : UMR0729
3 ASB - Analyse des Systèmes et Biométrie
Abstract : We study the stability loss delay phenomenon in a dynamic transcritical bifurcation in a class of three-dimensional prey and predator systems. The dynamics of the predator is assumed to be slow comparatively to the dynamics of the prey. As an application, a well-known model considered by Clark will be discussed.
Keywords : ASYMPTOTIC STABILITY DELAYED LOSS OF STABILITY SINGULAR PERTURBATIONS CANARDS BIOLOGICAL MODELS ECOLOGIE BIOLOGIE DES POPULATIONS STABILITE ASYMPTOTIQUE
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Journal articles
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https://hal.inria.fr/hal-00858536
Contributor : Alain Rapaport <>
Submitted on : Thursday, September 5, 2013 - 3:36:11 PM
Last modification on : Wednesday, February 10, 2021 - 3:35:52 AM

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Hafida Boudjellaba, Tewfik Sari. Dynamic transcritical bifurcations in a class of slow-fast predator-prey models. Journal of Differential Equations, Elsevier, 2009, 46 (6), pp.2205-2225. ⟨10.1016/j.jde.2009.01.001⟩. ⟨hal-00858536⟩

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