Europhys. Lett.
Volume 73, Number 3, February 2006
Page(s) 328 - 334
Section General
Published online 16 December 2005
Europhys. Lett., 73 (3), pp. 328-334 (2006)
DOI: 10.1209/epl/i2005-10400-0

The mean field of weakly coupled oscillators exhibits non-smooth phase noise

J. P. Gleeson

Department of Applied Mathematics, University College Cork - Cork, Ireland

received 1 September 2006; accepted in final form 30 November 2006
published online 16 December 2005

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 1/f 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 1/f scaling can also persist beyond the synchronization threshold.

05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
02.50.-r - Probability theory, stochastic processes, and statistics.

© EDP Sciences 2006