Volume 89, Number 1, January 2010
Article Number 10001
Number of page(s) 4
Section General
Published online 01 December 2009
EPL, 89 (2010) 10001
DOI: 10.1209/0295-5075/89/10001

Hyperbolic angular statistics for globally coupled phase oscillators

M.-O. Hongler1, R. Filliger2 and Ph. Blanchard1, 3

1   Ecole Polytechnique Fédérale EPFL - STI/IMT/LPM - Lausanne, Switzerland
2   Bern University of Applied Sciences - CH-2501 Biel, Switzerland
3   Fakultät für Physik and BiBos, Universität Bielefeld - Bielefeld, Germany, EU

received 29 November 2009; accepted in final form 9 December 2009; published January 2010
published online 22 December 2009

We analytically discuss a multiplicative noise generalization of the Kuramoto-Sakaguchi dynamics for an assembly of globally coupled phase oscillators. In the mean-field limit, the resulting class of invariant measures coincides with a generalized, two-parameter family of angular von Mises probability distributions which is governed by the exit law from the unit disc of a hyperbolic drifted Brownian motion. Our dynamics offers a simple yet analytically tractable generalization of Kuramoto-Sakaguchi dynamics with two control parameters. We derive an exact and very compact relation between the two control parameters at the onset of phase oscillators synchronization.

05.45.Xt - Synchronization; coupled oscillators.
05.10.Gg - Stochastic analysis methods (Fokker-Planck, Langevin, etc.).
02.50.Ey - Stochastic processes.

© EPLA 2010