Turbulence in the Ott-Antonsen equation for arrays of coupled phase oscillators
type: Item
instance of: scholarly article
zbMATH Open document ID: 1338.34080
DOI: 10.1088/0951-7715/29/2/257
published in: Nonlinearity
publication date: 2016-03-11T00:00:00Z
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34D06
Mathematics Subject Classification ID: 35B36
Mathematics Subject Classification ID: 45J05
zbMATH DE Number: 6554533
zbMATH Keywords: coupled oscillators
zbMATH Keywords: Ott/Antonsen
zbMATH Keywords: turbulence
zbMATH Keywords: Kuramoto model
zbMATH Keywords: twisted states
zbMATH Keywords: Benjamin-Feir instability
zbMATH Keywords: Eckhaus scenario
Wikidata QID: Q58160630
author: Matthias Wolfrum
author: S. V. Gurevich
author: Oleh Omel'chenko
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1088/0951-7715/29/2/257
OpenAlex ID: W2235848211
title: Turbulence in the Ott-Antonsen equation for arrays of coupled phase oscillators
review text: The authors consider a one-dimensional array of non-locally coupled heterogeneous phase oscillators. The coupling term between oscillators \(i\) and \(j\) is \(\sin{(\theta_i-\theta_j+\alpha)}\) where \(\theta_i\) is the phase of oscillator \(i\). By taking the continuum limit and using the Ott/Antonsen ansatz they derive an integro-differential evolution equation for the spatially-dependent Kuramoto order parameter. They analytically find and determine the stability of the incoherent state and of partially coherent plane waves with different wave numbers. Increasing the coupling strength for \(\alpha<\pi/4\) they find the appearance of partially coherent plane waves in the Eckhaus scenario. Increasing the coupling strength for \(\alpha>\pi/4\) they find that the incoherent state becomes unstable but no partially coherent plane waves are stable, as they have become unstable via a Benjamin-Feir instability. In this region either phase or amplitude turbulence are numerically observed. A codimension-two point at \(\alpha=\pi/4\) organises the possible dynamics.
reviewed by: Carlo Laing
description: scientific article; zbMATH DE number 6554533