Model reduction for the Kuramoto-Sakaguchi model: The importance of nonentrained rogue oscillators

Wenqi Yue, Lachlan D. Smith, and Georg A. Gottwald
Phys. Rev. E 101, 062213 – Published 23 June 2020

Abstract

The Kuramoto-Sakaguchi model for coupled phase oscillators with phase frustration is often studied in the thermodynamic limit of infinitely many oscillators. Here we extend a model reduction method based on collective coordinates to capture the collective dynamics of finite-size Kuramoto-Sakaguchi models. We find that the inclusion of the effects of rogue oscillators is essential to obtain an accurate description, in contrast to the original Kuramoto model, where we show that their effects can be ignored. We further introduce a more accurate ansatz function to describe the shape of synchronized oscillators. Our results from this extended collective coordinate approach reduce in the thermodynamic limit to the well-known mean-field consistency relations. For finite networks we show that our model reduction describes the collective behavior accurately, reproducing the order parameter, the mean frequency of the synchronized cluster, and the size of the cluster at a given coupling strength, as well as the critical coupling strength for partial and for global synchronization.

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  • Received 14 April 2020
  • Accepted 1 June 2020

DOI:https://doi.org/10.1103/PhysRevE.101.062213

©2020 American Physical Society

Physics Subject Headings (PhySH)

NetworksNonlinear Dynamics

Authors & Affiliations

Wenqi Yue*, Lachlan D. Smith, and Georg A. Gottwald

  • School of Mathematics and Statistics, The University of Sydney, Sydney, New South Wales, 2006 Australia

  • *wyue8667@uni.sydney.edu.au
  • lachlan.smith@sydney.edu.au
  • georg.gottwald@sydney.edu.au

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Vol. 101, Iss. 6 — June 2020

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