Delay stabilization of periodic orbits in coupled oscillator systems

作者：Fiedler B; Flunkert V; Hoevel P^*; Schoell E

来源：Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences, 2010, 368(1911): 319-341.

DOI：10.1098/rsta.2009.0232

• delay
• stabilization
• coupled oscillators
• Pyragas control

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.

• 出版日期2010-1-28