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Universality in the one-dimensional chain of phase-coupled oscillators

Lee, Tony E. and Refael, G. and Cross, M. C. and Kogan, Oleg and Rogers, Jeffrey L. (2009) Universality in the one-dimensional chain of phase-coupled oscillators. Physical Review E, 80 (4). Art. No. 046210 . ISSN 1539-3755. doi:10.1103/PhysRevE.80.046210.

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We apply a recently developed renormalization-group (RG) method to study synchronization in a one-dimensional chain of phase-coupled oscillators in the regime of weak randomness. The RG predicts how oscillators with randomly distributed frequencies and couplings form frequency-synchronized clusters. Although the RG was originally intended for strong randomness, i.e., for distributions with long tails, we find good agreement with numerical simulations even in the regime of weak randomness. We use the RG flow to derive how the correlation length scales with the width of the coupling distribution in the limit of large coupling. This leads to the identification of a universality class of distributions with the same critical exponent v. We also find universal scaling for small coupling. Finally, we show that the RG flow is characterized by a universal approach to the unsynchronized fixed point, which provides physical insight into low-frequency clusters.

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Additional Information:© 2009 The American Physical Society. Received 16 July 2009; published 21 October 2009. This work was supported by Boeing. G.R. thanks the Research Corporation and the Packard foundation for their generous support. We also thank Heywood Tam for many helpful discussions.
Funding AgencyGrant Number
Subject Keywords:critical exponents; oscillators; random processes; renormalisation; synchronisation
Issue or Number:4
Classification Code:PACS: 05.45.Xt; 89.75.-k.
Record Number:CaltechAUTHORS:20091124-144207656
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Official Citation:Universality in the one-dimensional chain of phase-coupled oscillators Tony E. Lee, G. Refael, M. C. Cross, Oleg Kogan, and Jeffrey L. Rogers, Phys. Rev. E 80, 046210 (2009), DOI:10.1103/PhysRevE.80.046210
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:16795
Deposited By: Tony Diaz
Deposited On:08 Dec 2009 20:07
Last Modified:08 Nov 2021 23:30

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