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Rich-club network topology to minimize synchronization cost due to phase difference among frequency-synchronized oscillators

Watanabe, T; (2013) Rich-club network topology to minimize synchronization cost due to phase difference among frequency-synchronized oscillators. Physica A: Statistical Mechanics and its Applications , 392 (5) pp. 1246-1255. 10.1016/j.physa.2012.11.041. Green open access

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Abstract

As exemplified by power grids and large-scale brain networks, some functions of networks consisting of phase oscillators rely on not only frequency synchronization, but also phase synchronization among the oscillators. Nevertheless, even after the oscillators reach frequency-synchronized status, the phase synchronization is not always accomplished because the phase difference among the oscillators is often trapped at non-zero constant values. Such phase difference potentially results in inefficient transfer of power or information among the oscillators, and avoids proper and efficient functioning of the networks. In the present study, we newly define synchronization cost by using the phase difference among the frequency-synchronized oscillators, and investigate the optimal network structure with the minimum synchronization cost through rewiring-based optimization. By using the Kuramoto model, we demonstrate that the cost is minimized in a network with a rich-club topology, which comprises the densely-connected center nodes and low-degree peripheral nodes connecting with the center module. We also show that the network topology is characterized by its bimodal degree distribution, which is quantified by Wolfson’s polarization index.

Type: Article
Title: Rich-club network topology to minimize synchronization cost due to phase difference among frequency-synchronized oscillators
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.physa.2012.11.041
Publisher version: http://dx.doi.org/10.1016/j.physa.2012.11.041
Language: English
Additional information: © 2013. This manuscript version is published under a Creative Commons Attribution Non-commercial Non-derivative 4.0 International licence (CC BY-NC-ND 4.0). This licence allows you to share, copy, distribute and transmit the work for personal and non-commercial use providing author and publisher attribution is clearly stated. Further details about CC BY licences are available at http://creativecommons.org/licenses/by/4.0.
Keywords: Synchrony; Electric grid; Brain network; Rewiring
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Brain Sciences
URI: https://discovery.ucl.ac.uk/id/eprint/1470605
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