Volume 73, Number 3, February 2006
|Page(s)||328 - 334|
|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: email@example.com
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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