Hyperbolic angular statistics for globally coupled phase oscillatorsM.-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.
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