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The Dynamical Impact of a Shortcut in Unidirectionally CoupledRings of Oscillators

Published online by Cambridge University Press:  17 September 2013

J.P. Pade ,
L. Lücken  and
S. Yanchuk
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Abstract

We study the destabilization mechanism in a unidirectional ring of identical oscillators,perturbed by the introduction of a long-range connection. It is known that for ahomogeneous, unidirectional ring of identical Stuart-Landau oscillators the trivialequilibrium undergoes a sequence of Hopf bifurcations eventually leading to thecoexistence of multiple stable periodic states resembling the Eckhaus scenario. We showthat this destabilization scenario persists under small non-local perturbations. In thiscase, the Eckhaus line is modulated according to certain resonance conditions. In the casewhen the shortcut is strong, we show that the coexisting periodic solutions split up intotwo groups. The first group consists of orbits which are unstable for all parametervalues, while the other one shows the classical Eckhaus behavior.

Keywords

network perturbationcoupled oscillatorssymmetry breakingshortcutunidirectional ring
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 5: Bifurcations , 2013 , pp. 173 - 189
Copyright
© EDP Sciences, 2013

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