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Title: Turbulence in the Ott-Antonsen equation for arrays of coupled phase oscillators
Authors: Wolfrum, MatthiasGurevich, Svetlana V.Omelchenko, Oleh E.
Issue Date: 2015
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 2135, ISSN 2198-5855
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: In this paper we study the transition to synchrony in an one-dimensional array of oscillators with non-local coupling. For its description in the continuum limit of a large number of phase oscillators, we use a corresponding Ott-Antonsen equation, which is an integrodifferential equation for the evolution of the macroscopic profiles of the local mean field. Recently, it has been reported that in the spatially extended case at the synchronization threshold there appear partially coherent plane waves with different wave numbers, which are organized in the well-known Eckhaus scenario. In this paper, we show that for Kuramoto-Sakaguchi phase oscillators the phase lag parameter in the interaction function can induce a Benjamin-Feir type instability of the partially coherent plane waves. The emerging collective macroscopic chaos appears as an intermediate stage between complete incoherence and stable partially coherent plane waves.We give an analytic treatment of the Benjamin-Feir instability and its onset in a codimension-two bifurcation in the Ott-Antonsen equation as well as a numerical study of the transition from phase turbulence to amplitude turbulence inside the Benjamin-Feir unstable region.
Keywords: Coupled oscillators; Kuramoto model; twisted states; turbulence; Ott/Antonsen; Eckhaus scenario
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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