Density of instantaneous frequencies in the Kuramoto-Sakaguchi model

We obtain a formula for the statistical distribution of instantaneous frequencies in the Kuramoto-Sakaguchi model. This work is based on the Kuramoto-Sakaguchi’s theory of globally coupled phase oscillators, which we review in full detail by discussing its assumptions and showing all steps behind the derivation of its main results. Our formula is a stationary probability density function with a complex mathematical structure, is consistent with numerical simulations and gives a description of the stationary collective states of the Kuramoto-Sakaguchi model.