Skip to Main content Skip to Navigation
Journal articles

The peaking phenomenon and singular perturbations

Claude Lobry 1 Tewfik Sari 2, 1 
1 MERE - Water Resource Modeling
CRISAM - Inria Sophia Antipolis - Méditerranée , INRA - Institut National de la Recherche Agronomique : UMR0729
Abstract : We study the asymptotic behaviour, when the parameter " tends to 0, of a class of singularly perturbed triangular systems x˙ = f(x, y), y˙ = G(y, "). We assume that all solutions of the second equation tend to zero arbitrarily fast when " tends to 0. We assume that the origin of equation x˙ = f(x, 0) is globally asymptotically stable. Some states of the second equation may peak to very large values, before they rapidly decay to zero. Such peaking states can destabilize the first equation. The paper introduces the concept of instantaneous stability, to measure the fast decay to zero of the solutions of the second equation, and the concept of uniform infinitesimal boundedness to measure the effects of peaking on the first equation. Whe show that all the solutions of the triangular system tend to zero when " ! 0 and t ! +1. Our results are formulated in both classical mathematics and nonstandard analysis.
Document type :
Journal articles
Complete list of metadata

Cited literature [11 references]  Display  Hide  Download
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Tuesday, February 23, 2016 - 1:45:57 PM
Last modification on : Thursday, March 10, 2022 - 5:58:02 PM
Long-term archiving on: : Tuesday, May 24, 2016 - 1:12:42 PM


Publisher files allowed on an open archive




Claude Lobry, Tewfik Sari. The peaking phenomenon and singular perturbations. Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, INRIA, 2008, Volume 9, 2007 Conference in Honor of Claude Lobry, 2008 (Spécial issue of Claude Lobry), pp.487-516. ⟨10.46298/arima.1910⟩. ⟨hal-01019722v2⟩



Record views


Files downloads