Delay stabilization of periodic orbits in coupled oscillator systems-Reference-Cited by-同舟云学术

Delay stabilization of periodic orbits in coupled oscillator systems

Published:2010-01-28 Issue:1911 Volume:368 Page:319-341
ISSN:1364-503X
Container-title:Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Phil. Trans. R. Soc. A.

Author:

Fiedler B.¹,Flunkert V.²,Hövel P.²,Schöll E.²

Affiliation:

1. Institut für Mathematik I, Free Universität Berlin, Arnimallee 2-6, 14195 Berlin, Germany

2. Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 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.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2009.0232

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