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Frequency precision of two-dimensional lattices of coupled oscillators with spiral patterns

Allen, John-Mark A. and Cross, M. C. (2013) Frequency precision of two-dimensional lattices of coupled oscillators with spiral patterns. Physical Review E, 87 (5). Art. No. 052902. ISSN 1539-3755. doi:10.1103/PhysRevE.87.052902.

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Two-dimensional lattices of N synchronized oscillators with reactive coupling are considered as high-precision frequency sources in the case where a spiral pattern is formed. The improvement of the frequency precision is shown to be independent of N for large N, unlike the case of purely dissipative coupling where the improvement is proportional to N, but instead depends on just those oscillators in the core of the spiral that acts as the source region of the waves. Our conclusions are based on numerical simulations of up to N = 29 929 oscillators and analytic results for a continuum approximation to the lattice in an infinite system. We derive an expression for the dependence of the frequency precision on the reactive component of the coupling constant, depending on a single parameter given by fitting the frequency of the spiral waves to the numerical simulations.

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Additional Information:© 2013 American Physical Society. Received 7 March 2013; published 8 May 2013. This material is based upon work supported by the National Science Foundation under Grant No. DMR-1003337. J.M.A.A. is supported by the Master and Fellows of Corpus Christi College and the California Institute of Technology.
Funding AgencyGrant Number
Corpus Christi College Master and FellowsUNSPECIFIED
Issue or Number:5
Classification Code:PACS: 05.45.Xt, 87.19.lm, 89.75.Kd
Record Number:CaltechAUTHORS:20130619-111712761
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38984
Deposited By: Tony Diaz
Deposited On:24 Jun 2013 16:32
Last Modified:09 Nov 2021 23:41

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