Model reduction for the collective dynamics of globally coupled oscillators: From finite networks to the thermodynamic limit

Model reduction techniques have been widely used to study the collective behavior of globally coupled oscillators. However, most approaches assume that there are infinitely many oscillators. Here, we propose a new ansatz, based on the collective coordinate approach, that reproduces the collective dy...

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Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 2020-09, Vol.30 (9), p.093107-093107
Main Authors: Smith, Lachlan D., Gottwald, Georg A.
Format: Article
Language:English
Subjects:
Bifurcations
Model accuracy
Model reduction
Order parameters
Oscillators
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Summary:Model reduction techniques have been widely used to study the collective behavior of globally coupled oscillators. However, most approaches assume that there are infinitely many oscillators. Here, we propose a new ansatz, based on the collective coordinate approach, that reproduces the collective dynamics of the Kuramoto model for finite networks to high accuracy, yields the same bifurcation structure in the thermodynamic limit of infinitely many oscillators as previous approaches, and additionally captures the dynamics of the order parameter in the thermodynamic limit, including critical slowing down that results from a cascade of saddle-node bifurcations.
ISSN:1054-1500
1089-7682
DOI:10.1063/5.0009790