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Synchronization of oscillators with long-range power law interactions

Chowdhury, Debanjan and Cross, M. C. (2010) Synchronization of oscillators with long-range power law interactions. Physical Review E, 82 (1). Art. No. 016205 . ISSN 1539-3755.

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We present analytical calculations and numerical simulations for the synchronization of oscillators interacting via a long-range power law interaction on a one-dimensional lattice. We have identified the critical value of the power law exponent α_c across which a transition from a synchronized to an unsynchronized state takes place for a sufficiently strong but finite coupling strength in the large system limit. We find α_c=3/2. Frequency entrainment and phase ordering are discussed as a function of α≥1. The calculations are performed using an expansion about the aligned phase state (spin-wave approximation) and a coarse graining approach. We also generalize the spin-wave results to the d-dimensional problem.

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Additional Information:© 2010 The American Physical Society. Received 25 March 2010; published 9 July 2010. We thank Gil Refael, Tony Lee and Hsin-hua Lai for interesting discussions. D.C. thanks the IIT Kanpur-Caltech MoU and the SURF program at Caltech for financial support.
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SURF program at CaltechUNSPECIFIED
Issue or Number:1
Classification Code:PACS: 05.45.Xt, 89.75.-k
Record Number:CaltechAUTHORS:20100803-145013910
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19263
Deposited By: Tony Diaz
Deposited On:03 Aug 2010 22:28
Last Modified:03 Oct 2019 01:54

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