Pseudospectra and delay differential equations

K Green; T Wagenknecht

Pseudospectra and delay differential equations

K Green
, T Wagenknecht

Research output: Working paper

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Abstract

In this paper we present a new method for computing the pseudospectra of delay di erential equations (DDEs) with fixed finite delay. This provides information on the sensitivity of eigenvalues under arbitrary perturbations of a given size, and hence insight into how stability may change under variation of parameters. We also investigate how di erent weighted perturbations applied to the two matrices of the delayed eigenvalue problem a ect the pseudospectrum. To illustrate our method, we consider a DDE modelling a semiconductor laser subject to phase-conjugate feedback.

Original language	English
Publication status	Unpublished - 2004

Bibliographical note

Sponsorship: The authors would like to thank A. R. Champneys and M. I. Friswell for helpful comments on a draft version of this paper. This research was supported by the EPSRC grant GR/535684/01.

Keywords

phase-conjugate feedback laser
transient response
sensitivity to perturbation

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2004r27Submitted manuscript, 2.67 MB

http://hdl.handle.net/1983/110

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1 Article (Academic Journal)

Pseudospectra and delay differential equations
Green, K. & Wagenknecht, T., 2006, In: Journal of Computational and Applied Mathematics.
Research output: Contribution to journal › Article (Academic Journal) › peer-review

Cite this

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title = "Pseudospectra and delay differential equations",

abstract = "In this paper we present a new method for computing the pseudospectra of delay di erential equations (DDEs) with fixed finite delay. This provides information on the sensitivity of eigenvalues under arbitrary perturbations of a given size, and hence insight into how stability may change under variation of parameters. We also investigate how di erent weighted perturbations applied to the two matrices of the delayed eigenvalue problem a ect the pseudospectrum. To illustrate our method, we consider a DDE modelling a semiconductor laser subject to phase-conjugate feedback.",

keywords = "phase-conjugate feedback laser, transient response, sensitivity to perturbation",

author = "K Green and T Wagenknecht",

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T1 - Pseudospectra and delay differential equations

AU - Green, K

AU - Wagenknecht, T

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PY - 2004

Y1 - 2004

N2 - In this paper we present a new method for computing the pseudospectra of delay di erential equations (DDEs) with fixed finite delay. This provides information on the sensitivity of eigenvalues under arbitrary perturbations of a given size, and hence insight into how stability may change under variation of parameters. We also investigate how di erent weighted perturbations applied to the two matrices of the delayed eigenvalue problem a ect the pseudospectrum. To illustrate our method, we consider a DDE modelling a semiconductor laser subject to phase-conjugate feedback.

AB - In this paper we present a new method for computing the pseudospectra of delay di erential equations (DDEs) with fixed finite delay. This provides information on the sensitivity of eigenvalues under arbitrary perturbations of a given size, and hence insight into how stability may change under variation of parameters. We also investigate how di erent weighted perturbations applied to the two matrices of the delayed eigenvalue problem a ect the pseudospectrum. To illustrate our method, we consider a DDE modelling a semiconductor laser subject to phase-conjugate feedback.

KW - phase-conjugate feedback laser

KW - transient response

KW - sensitivity to perturbation

M3 - Working paper

BT - Pseudospectra and delay differential equations

ER -

Pseudospectra and delay differential equations

Abstract

Bibliographical note

Keywords

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Research output

Pseudospectra and delay differential equations

Cite this