Pseudospectra and delay differential equations

K. Green, T. Wagenknecht

    Research output: Contribution to JournalArticleAcademicpeer-review

    Abstract

    In this paper, we present a new method for computing the pseudospectra of delay differential 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 differently weighted perturbations applied to the individual matrices of the delayed eigenvalue problem affect the pseudospectra. Furthermore, we compute pseudospectra of the infinitesimal generator of the DDE, from which a lower bound on the maximum transient growth can be inferred. To illustrate our method, we consider a DDE modelling a semiconductor laser subject to external feedback. © 2005 Elsevier B.V. All rights reserved.
    Original languageEnglish
    Pages (from-to)567-578
    JournalJournal of computational and applied mathematics
    Volume196
    Issue number2
    DOIs
    Publication statusPublished - 2006

    Bibliographical note

    Pseudospectra and delay differential equations

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