Time transformations for delay differential equations

Brunner, Hermann and Maset, Stefano (2009) Time transformations for delay differential equations. Discrete and Continuous Dynamical Systems. Series A , 25 (3). pp. 751-775. ISSN 1553-5231

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Abstract

We study changes of variable, called time transformations, which reduce a delay differential equation (DDE) with a variable non-vanishing delay and an unbounded lag function to another DDE with a constant delay. By using this reduction, we can easily obtain a superconvergent integration of the original equation, even in the case of a non-strictly-increasing lag function, and study the type of decay to zero of solutions of scalar linear non-autonomous equations with a strictly increasing lag function.

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