Time scales in linear delayed differential equations

This paper is devoted to the loving memory of our friend Ovide Arino, who passed away during the production of it
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Abstract

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 ε>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 ε0 to the solution of an aggregated system whose construction is proposed.

Keywords

Singular perturbations
Aggregation of variables
Delayed differential equations
Two time scales

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Research of authors E. Sánchez, R. Bravo de la Parra and P. Gómez-Mourelo supported by MCYT grant MTM2005-00423, and FEDER.