A shocking display of synchrony

This article explores the Kuramoto model describing the synchronization of a population of coupled oscillators. Two versions of this model are conside red: a discrete version suitable for a population with a finite number of o scillators, and a continuum model found in the limit of an infinite populat ion. When the strength of the coupling between the oscillators exceeds a th reshold, the oscillators partially synchronize. We explore the transition i n the continuum model, which takes the form of a bifurcation of a discrete mode from a continuous spectrum. We use numerical methods and perturbation theory to study the patterns of synchronization that form beyond transition , and compare with the synchronization predicted by the discrete model. The re are similarities with instabilities in ideal plasmas and inviscid fluids , but these are superficial. (C) 2000 Published by Elsevier Science B.V.