Beyond the odd number limitation: a bifurcation analysis of time-delayed feedback control.
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.
Just
W
W
School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, United Kingdom. w.just@qmul.ac.uk
Fiedler
B
B
Georgi
M
M
Flunkert
V
V
Hövel
P
P
Schöll
E
E