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

Authors:
Kirk Green;Bernd Krauskopf;Koen Engelborghs
Affiliations:
Department of Computer Science, K.U. Leuven, Celestijnenlaan 200A, 3001 Heverlee, Belgium;Department of Engineering Mathematics, University of Bristol, Bristol BS8 1TR, UK;Department of Computer Science, K.U. Leuven, Celestijnenlaan 200A, 3001 Heverlee, Belgium
Venue:
Journal of Computational Physics
Year:
2004

Citing 3
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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 an established algorithm for computing one-dimensional (1D) unstable manifolds of an associated saddle fixed point of a suitable Poincaré 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.