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.
Author: | Mark Lichtner, Matthias Wolfrum, Serhiy Yanchuk |
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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 |