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The spectrum of delay differential equations with large delay

Please always quote using this URN:urn:nbn:de:0296-matheon-6440
  • We show that the spectrum of linear delay differential equations with large delay splits into two different parts. One part, called the strong spectrum, converges to isolated points when the delay parameter tends to infinity. The other part, called the pseudocontinuous spectrum, accumulates near criticality and converges after rescaling to a set of spectral curves, called the asymptotic continuous spectrum. We show that the spectral curves and strong spectral points provide a complete description of the spectrum for sufficiently large delay and can be comparatively easily calculated by approximating expressions.

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Metadaten
Author:Mark Lichtner, Matthias Wolfrum, Serhiy Yanchuk
URN:urn:nbn:de:0296-matheon-6440
Referee:Volker Mehrmann
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2009/07/30
Release Date:2009/07/29
Tag:
Institute:Humboldt-Universität zu Berlin
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Kxx Functional-differential and differential-difference equations [See also 37-XX] / 34K06 Linear functional-differential equations
34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Kxx Functional-differential and differential-difference equations [See also 37-XX] / 34K20 Stability theory
Preprint Number:647
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