https://doi.org/10.1140/epjst/e2010-01341-9
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Beyond the odd number limitation of time-delayed feedback control of periodic orbits
1 Institut für Mathematik I, FU Berlin,
Arnimallee 2-6,
14195
Berlin,
Germany
2 Institut für Theoretische Physik,
Technische Universität Berlin,
Hardenbergstraße 36,
10623
Berlin,
Germany
Received:
22
November
2010
Revised:
23
December
2010
Published online:
18
February
2011
We discuss the stabilization of odd-number orbits by time-delayed feedback control. In particular, we review the stabilization of odd-number orbits born in a subcritical Hopf bifurcation or a saddle-node bifurcation of periodic orbits. These examples refute the often invoked odd-number theorem.
© EDP Sciences, Springer-Verlag, 2011