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

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.