Dresden 2009 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 26: Poster II
DY 26.14: Poster
Donnerstag, 26. März 2009, 16:00–18:00, P1A
Delay stabilization of rotating waves near fold bifurcation and application to all-optical control of a semiconductor laser — Bernold Fiedler1, Serhiy Yanchuk2, Valentin Flunkert3, Hans-Jürgen Wünsche4, •Philipp Hövel3, and Eckehard Schöll3 — 1Institut für Mathematik I, FU Berlin, Arnimallee 2-6, D-14195 Berlin, Germany — 2Humboldt Universität zu Berlin, Institut für Mathematik, Rudower Chaussee 25, D-12489 Berlin, Germany — 3Institut f. Theo. Physik, Sekr. EW 7-1, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany — 4Humboldt Universität zu Berlin, Institut für Physik, Newtonstr. 15, D-12489 Berlin, Germany
We consider the delayed feedback control method for stabilization of unstable rotating waves near a fold bifurcation. Theoretical analysis of a generic model and numerical bifurcation analysis of the rate-equations model demonstrate that such orbits can always be stabilized by a proper choice of control parameters. We confirm the recently discovered invalidity of the so-called “odd-number-limitation” of delayed feedback control. Previous results have been restricted to the vicinity of a subcritical Hopf bifurcation. We now refute such a limitation for rotating waves near a fold bifurcation. We include an application to all-optical realization of the control in three-section semiconductor lasers.