| Issue |
Europhys. Lett.
Volume 73, Number 3, February 2006
|
|
|---|---|---|
| Page(s) | 328 - 334 | |
| Section | General | |
| DOI | https://doi.org/10.1209/epl/i2005-10400-0 | |
| Published online | 16 December 2005 | |
The mean field of weakly coupled oscillators exhibits non-smooth phase noise
Department of Applied Mathematics, University College Cork - Cork, Ireland
Corresponding author: j.gleeson@ucc.ie
Received:
1
September
2006
Accepted:
30
November
2006
The magnitude of the complex-valued mean field of N coupled
oscillators is known to act as an order parameter for the
synchronization transition; in this letter it is shown that the
phase speed (rate of change of the phase angle) of the mean field
is a non-smooth random process, as demonstrated by the existence
of a 
spectrum across a range of frequencies. An exact
expression for the phase speed correlation function is derived in
the limit of vanishing coupling between oscillators; numerical
results show the scaling can also
persist beyond the synchronization threshold.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 02.50.-r – Probability theory, stochastic processes, and statistics
© EDP Sciences, 2006
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