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Title: Partially coherent twisted states in arrays of coupled phase oscillators
Authors: Omel'chenko, OlehWolfrum, MatthiasLaing, Carlo
Issue Date: 2013
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 1908, 2198-5855
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: We consider a one-dimensional array of phase oscillators with non-local coupling and a Lorenztian distribution of natural frequencies. The primary objects of interest are partially coherent states that are uniformly twisted in space. To analyze these we take the continuum limit, perform an Ott/Antonsen reduction, integrate over the natural frequencies and study the resulting spatio-temporal system on an unbounded domain. We show that these twisted states and their stability can be calculated explicitly. We find that stable twisted states with different wave numbers appear for increasing coupling strength in the wellknown Eckhaus scenario. Simulations of finite arrays of oscillators show good agreement with results of the analysis of the infinite system.
Keywords: Coupled oscillators; Kuramoto model; twisted states; Ott/Antonsen; Eckhaus bifurcation
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
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Appears in Collections:Mathematik



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