Dynamics of order parameters for a population of globally coupled oscillators

Abstract

Using an expansion in order parameters, the equation of motion for the centroid of globally coupled oscillators with natural frequencies taken from a distribution is obtained for the case of high coupling, low dispersion of natural frequencies and any number of oscillators. To the first order, the system can be approximated by a set of four equations, where the centroid is coupled with a second macroscopic variable, which describes the dynamics of the oscillators around their average. This gives rise to collective effects that suggest experiments aimed at measuring the parameters of the population.