On the complete phase synchronization for the Kuramoto model in the   mean-field limit
  We study the Kuramoto model for coupled oscillators. For the case of identical natural frequencies, we give a new proof of the complete frequency synchronization for all initial data; extending this result to the continuous version of the model, we manage to prove the complete phase synchronization for any non-atomic measure-valued initial datum. We also discuss the relation between the boundedness of the entropy and the convergence to an incoherent state, for the case of non identical natural frequencies. 
Dario Benedetto, Emanuele Caglioti, Umberto Montemagno
math.AP