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arXiv · 0911.4699

Hyperbolic angular statistics for globally coupled phase oscillators

M. -O. Hongler·R. Filliger·Ph. Blanchard
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Abstract

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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M. -O. Hongler, R. Filliger, Ph. Blanchard. 2009-11-24. Hyperbolic angular statistics for globally coupled phase oscillators. https://doi.org/10.1209/0295-5075%2F89%2F10001

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