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 http://resolver.caltech.edu/CaltechAUTHORS:20091124-144207656
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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.
|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.|
|Subject Keywords:||critical exponents; oscillators; random processes; renormalisation; synchronisation|
|Classification Code:||PACS: 05.45.Xt; 89.75.-k.|
|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.|
|Deposited By:||Tony Diaz|
|Deposited On:||08 Dec 2009 20:07|
|Last Modified:||26 Dec 2012 11:34|
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