Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4643362 | Journal of Computational and Applied Mathematics | 2006 | 12 Pages |
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Kirk Green, Thomas Wagenknecht,