Pseudospectra and delay differential equations

K Green, T Wagenknecht

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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 languageEnglish
Publication statusUnpublished - 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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