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Improving the frequency precision of oscillators by synchronization

Cross, M. C. (2012) Improving the frequency precision of oscillators by synchronization. Physical Review E, 85 (4). Art. No. 046214 . ISSN 1539-3755.

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Improving the frequency precision by synchronizing a lattice of N oscillators with disparate frequencies is studied in the phase reduction limit. In the general case where the coupling is not purely dissipative the synchronized state consists of targetlike waves radiating from a local source, which is a region of higher-frequency oscillators. In this state the improvement of the frequency precision is shown to be independent of N for large N, but instead depends on the disorder and reflects the dependence of the frequency of the synchronized state on just those oscillators in the source region of the waves. These results are obtained by a mapping of the nonlinear phase dynamics onto the linear Anderson problem of the quantum mechanics of electrons on a random lattice in the tight-binding approximation.

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Additional Information:© 2012 American Physical Society. Received 21 September 2011; published 19 April 2012. This work was supported by National Science Foundation Grant No. DMR-1003337. I thank Eyal Kenig and Tony Lee for comments on the manuscript.
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Issue or Number:4
Classification Code:PACS: 05.45.Xt, 87.19.lm, 89.75.Kd
Record Number:CaltechAUTHORS:20120511-101600990
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:31429
Deposited By: Tony Diaz
Deposited On:11 May 2012 18:44
Last Modified:03 Oct 2019 03:51

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