%0 Journal Article
%9 ACL : Articles dans des revues avec comité de lecture répertoriées par l'AERES
%A Sanchez, E.
%A De la Parra, R.B.
%A Auger, Pierre
%A Gomez Mourelo, P.
%T Time scales in linear delayed differential equations
%D 2006
%L fdi:010037626
%G ENG
%J Journal of Mathematical Analysis and Applications
%@ 0022-247X
%K singular perturbations ; aggregation of variables ; delayed differential equations ; two time scales
%M CC:0002405660-0053
%N 1
%P 680-699
%R 10.1016/j.jmaa.2005.10.074
%U https://www.documentation.ird.fr/hor/fdi:010037626
%> https://www.documentation.ird.fr/intranet/publi/2006/10/010037626.pdf
%V 323
%W Horizon (IRD)
%X The aim of this paper is to apply and justify the so-called aggregation of variables method for reduction of a complex system of linear delayed differential equations with two time scales: slow and fast. The difference between these time scales makes a parameter epsilon > 0 to appear in the formulation, being a mathematical problem of singular perturbations. The main result of this work consists of demonstrating that, under some hypotheses, the solution to the perturbed problem converges when epsilon -> 0 to the solution of an aggregated system whose construction is proposed. (c) 2005 Elsevier Inc. All rights reserved.
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