TY - JOUR
T1 - Pseudospectra and delay differential equations
AU - Green, K.
AU - Wagenknecht, T.
N1 - Pseudospectra and delay differential equations
PY - 2006
Y1 - 2006
N2 - 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.
AB - 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.
U2 - 10.1016/j.cam.2005.10.011
DO - 10.1016/j.cam.2005.10.011
M3 - Article
VL - 196
SP - 567
EP - 578
JO - Journal of computational and applied mathematics
JF - Journal of computational and applied mathematics
SN - 0377-0427
IS - 2
ER -