| Issue |
EPL
Volume 89, Number 1, January 2010
|
|
|---|---|---|
| Article Number | 10001 | |
| Number of page(s) | 4 | |
| Section | General | |
| DOI | https://doi.org/10.1209/0295-5075/89/10001 | |
| Published online | 01 December 2009 | |
Hyperbolic angular statistics for globally coupled phase oscillators
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
Corresponding author: roger.filliger@bfh.ch
Received:
29
November
2009
Accepted:
9
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.
PACS: 05.45.Xt – Synchronization; coupled oscillators / 05.10.Gg – Stochastic analysis methods (Fokker-Planck, Langevin, etc.) / 02.50.Ey – Stochastic processes
© EPLA, 2010
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