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Delay stabilization of rotating waves near fold bifurcation and application to all-optical control of a semiconductor
B Fiedler1, S Yanchuk, V Flunkert
1Institut für Mathematik I, FU Berlin, Arnimallee 2-6, D-14195 Berlin, Germany.
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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