Delay stabilization of rotating waves near fold bifurcation and application to all-optical control of a semiconductor laser.
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.
Fiedler
B
B
Institut für Mathematik I, FU Berlin, Arnimallee 2-6, D-14195 Berlin, Germany.
Yanchuk
S
S
Flunkert
V
V
Hövel
P
P
Wünsche
H-J
HJ
Schöll
E
E