One-dimensional unstable eigenfunction and manifold computations in delay differential equations

K Green; B Krauskopf; Koen Engelborghs

doi:10.1016/j.jcp.2003.11.018

One-dimensional unstable eigenfunction and manifold computations in delay differential equations

K Green, B Krauskopf, Koen Engelborghs

Department of Engineering Mathematics

Research output: Working paper

14 Citations (Scopus)

373 Downloads (Pure)

Abstract

In this paper we present a new numerical technique for computing the unstable eigenfunctions of a saddle periodic orbit in a delay differential equation. This is used to obtain the necessary starting data for the computation of one-dimensional unstable manifolds of an associated saddle fixed point of a suitable Poincar\'e map. To illustrate our method, we investigate an intermittent transition to chaos in a delay system describing a semiconductor laser subject to phase-conjugate feedback. of

Original language	English
DOIs	https://doi.org/10.1016/j.jcp.2003.11.018
Publication status	Unpublished - 2004

Bibliographical note

Additional information: Later publised by Elsevier Science, (2004) Journal of Computational Physics, 197 (1), pp. 86-98. ISSN 0021-9991

Keywords

Intermittent transition
Numerical tools for DDEs
PCF laser

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10.1016/j.jcp.2003.11.018

Udp main rev4Submitted manuscript, 1.36 MB

http://hdl.handle.net/1983/76

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14 Citations
1 Article (Academic Journal)

One-dimensional unstable eigenfunction and manifold computations in delay differential equations
Green, K., Krauskopf, B. & Engelborghs, K., 2004, In: Journal of Computational Physics. 197(1), p. 86 - 98
Research output: Contribution to journal › Article (Academic Journal) › peer-review

Cite this

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abstract = "In this paper we present a new numerical technique for computing the unstable eigenfunctions of a saddle periodic orbit in a delay differential equation. This is used to obtain the necessary starting data for the computation of one-dimensional unstable manifolds of an associated saddle fixed point of a suitable Poincar\'e map. To illustrate our method, we investigate an intermittent transition to chaos in a delay system describing a semiconductor laser subject to phase-conjugate feedback. of",

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AU - Krauskopf, B

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PY - 2004

Y1 - 2004

N2 - In this paper we present a new numerical technique for computing the unstable eigenfunctions of a saddle periodic orbit in a delay differential equation. This is used to obtain the necessary starting data for the computation of one-dimensional unstable manifolds of an associated saddle fixed point of a suitable Poincar\'e map. To illustrate our method, we investigate an intermittent transition to chaos in a delay system describing a semiconductor laser subject to phase-conjugate feedback. of

AB - In this paper we present a new numerical technique for computing the unstable eigenfunctions of a saddle periodic orbit in a delay differential equation. This is used to obtain the necessary starting data for the computation of one-dimensional unstable manifolds of an associated saddle fixed point of a suitable Poincar\'e map. To illustrate our method, we investigate an intermittent transition to chaos in a delay system describing a semiconductor laser subject to phase-conjugate feedback. of

KW - Intermittent transition

KW - Numerical tools for DDEs

KW - PCF laser

U2 - 10.1016/j.jcp.2003.11.018

DO - 10.1016/j.jcp.2003.11.018

M3 - Working paper

BT - One-dimensional unstable eigenfunction and manifold computations in delay differential equations

ER -

One-dimensional unstable eigenfunction and manifold computations in delay differential equations

Abstract

Bibliographical note

Keywords

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Research output

One-dimensional unstable eigenfunction and manifold computations in delay differential equations

Cite this