Hyperbolic angular statistics for globally coupled oscillators
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.
Record created on 2009-12-29, modified on 2016-08-08