Pseudospectra and delay differential equations

Authors:
Kirk Green;Thomas Wagenknecht
Affiliations:
Bristol Laboratory for Advanced Dynamics Engineering, University of Bristol, Bristol, UK and Theoretical Physics, FEW, Vrije Universiteit, Amsterdam, The Netherlands;Bristol Laboratory for Advanced Dynamics Engineering, University of Bristol, Bristol, UK
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

Citing 6
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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.