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Renormalization group approach to oscillator synchronization

Kogan, Oleg and Rogers, Jeffrey L. and Cross, M. C. and Refael, G. (2009) Renormalization group approach to oscillator synchronization. Physical Review E, 80 (3). Art. No. 036206. ISSN 1539-3755. doi:10.1103/PhysRevE.80.036206.

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We develop a renormalization group method to investigate synchronization clusters in a one-dimensional chain of nearest-neighbor coupled phase oscillators. The method is best suited for chains with strong disorder in the intrinsic frequencies and coupling strengths. The results are compared with numerical simulations of the chain dynamics and good agreement in several characteristics is found. We apply the renormalization group and simulations to Lorentzian distributions of intrinsic frequencies and couplings and investigate the statistics of the resultant cluster sizes and frequencies, as well as the dependence of the characteristic cluster length upon parameters of these Lorentzian distributions.

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Additional Information:© 2009 The American Physical Society. Received 27 October 2008; published 18 September 2009. It is a pleasure to thank Heywood Tam for numerous discussions and Tony Lee for carefully checking the RG procedure. We are also grateful to Boeing and the National Science Foundation under Grant No. DMR-0314069 for funding this work.
Funding AgencyGrant Number
Subject Keywords:nonlinear dynamical systems; oscillators; renormalisation; synchronisation
Issue or Number:3
Classification Code:PACS numbers: 05.45.Xt, 05.10.Cc, 89.75.Kd, 89.75.Fb.
Record Number:CaltechAUTHORS:20091020-134924682
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Official Citation:Renormalization group approach to oscillator synchronization Oleg Kogan, Jeffrey L. Rogers, M. C. Cross, and G. Refael, Phys. Rev. E 80, 036206 (2009), DOI:10.1103/PhysRevE.80.036206
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:16410
Deposited By: Tony Diaz
Deposited On:21 Oct 2009 17:38
Last Modified:08 Nov 2021 23:26

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