Eur. Phys. J. Special Topics 191, 53-70 (2010)
https://doi.org/10.1140/epjst/e2010-01341-9

Minireview

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

Abstract

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.