Dynamics of order parameters for globally coupled oscillators

The equation of motion for the centroid of globally coupled oscillators with natural frequency mismatch is obtained through a series expansion in order parameters, valid for any population size. In the case of strong coupling and narrow-frequency distribution the first-order expansion (corresponding to a system where the centroid is coupled to a second macroscopic variable), predicts transient and asymptotic properties of the dynamics of the centroid. Phase transitions appear as macroscopic bifurcations. Collective properties arising in the transient, and particularly critical perturbations, suggest a method of experimental relevance for identifying the parameters of the population.