Hyperbolic angular statistics for globally coupled phase oscillators

Details Hyperbolic angular statistics for globally coupled phase oscillators Hyperbolic angular statistics for globally coupled phase oscillators

2009-11-24

arxiv.org/abs/0911.4699v1

Physics

Condensed Matter

Statistical Mechanics

8 pages

Scientific paper

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.

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