Delay stabilization of periodic orbits in coupled oscillator systems.
We study diffusively coupled oscillators in Hopf normal form. By introducing a non-invasive delay coupling, we are able to stabilize the inherently unstable anti-phase orbits. For the super- and subcritical cases, we state a condition on the oscillator's nonlinearity that is necessary and sufficient to find coupling parameters for successful stabilization. We prove these conditions and review previous results on the stabilization of odd-number orbits by time-delayed feedback. Finally, we illustrate the results with numerical simulations.
Fiedler
B
B
Institut für Mathematik I, Free Universität Berlin, Arnimallee 2-6, 14195 Berlin, Germany.
Flunkert
V
V
Hövel
P
P
Schöll
E
E
D000465:Algorithms; D005246:Feedback; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000706:statistics & numerical data*; D010507:Periodicity; D013598:Systems Theory; D013997:Time Factors