title: Delay stabilization of periodic orbits in coupled oscillator systems.
abstract: 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.
authors.affiliation: Institut für Mathematik I, Free Universität Berlin, Arnimallee 2-6, 14195 Berlin, Germany.
authors.forename: B
authors.initials: B
authors.lastname: Fiedler
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
mesh_terms: D000465:Algorithms; D005246:Feedback; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000706:statistics & numerical data*; D010507:Periodicity; D013598:Systems Theory; D013997:Time Factors