title: Beyond the odd number limitation: a bifurcation analysis of time-delayed feedback control.
abstract: We investigate the normal form of a subcritical Hopf bifurcation subjected to time-delayed feedback control. Bifurcation diagrams which cover time-dependent states as well are obtained by analytical means. The computations show that unstable limit cycles with an odd number of positive Floquet exponents can be stabilized by time-delayed feedback control, contrary to incorrect claims in the literature. The model system constitutes one of the few examples where a nonlinear time delay system can be treated entirely by analytical means.
authors.affiliation: School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, United Kingdom. w.just@qmul.ac.uk
authors.forename: W
authors.initials: W
authors.lastname: Just
authors.forename: B
authors.initials: B
authors.lastname: Fiedler
authors.forename: M
authors.initials: M
authors.lastname: Georgi
authors.forename: V
authors.initials: V
authors.lastname: Flunkert
authors.forename: P
authors.initials: P
authors.lastname: Hövel
authors.forename: E
authors.initials: E
authors.lastname: Schöll