Journal
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 368, Issue 1911, Pages 319-341Publisher
ROYAL SOC
DOI: 10.1098/rsta.2009.0232
Keywords
delay; stabilization; coupled oscillators; Pyragas control
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Funding
- Deutsche Forschungsgemeinschaft [Sfb 555]
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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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