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