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Delay stabilization of periodic orbits in coupled oscillator systems
B Fiedler1, V Flunkert, P Hövel
1Institut für Mathematik I, Free Universität Berlin, Arnimallee 2-6, 14195 Berlin, Germany.
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.
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