Delay stabilization of rotating waves near fold bifurcation and application to all-optical control of a semiconductor laser

B. Fiedler, S. Yanchuk, V. Flunkert, P. Hövel, H.-J. Wünsche, and E. Schöll
Phys. Rev. E 77, 066207 – Published 10 June 2008

Abstract

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. Our paper confirms 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.

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  • Received 18 February 2008

DOI:https://doi.org/10.1103/PhysRevE.77.066207

©2008 American Physical Society

Authors & Affiliations

B. Fiedler1, S. Yanchuk2,3, V. Flunkert4, P. Hövel4, H.-J. Wünsche5, and E. Schöll4

  • 1Institut für Mathematik I, FU Berlin, Arnimallee 2-6, D-14195 Berlin, Germany
  • 2Weierstraß Institut für Angewandte Analysis and Stochastik, Mohrenstraße 39, D-10117 Berlin, Germany
  • 3Humboldt Universität zu Berlin, Institut für Mathematik, Rudower Chaussee 25, D-12489 Berlin, Germany
  • 4Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, D-10623 Berlin, Germany
  • 5Humboldt Universität zu Berlin, Institut für Physik, Newtonstrße 15, D-12489 Berlin, Germany

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Issue

Vol. 77, Iss. 6 — June 2008

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