Communications in Mathematical Sciences

Volume 13 (2015)

Number 7

On the complete phase synchronization for the Kuramoto model in the mean-field limit

Pages: 1775 – 1786

DOI: https://dx.doi.org/10.4310/CMS.2015.v13.n7.a6

Authors

Dario Benedetto (Dipartimento di Matematica, Sapienza Università di Roma, Italy)

Emanuele Caglioti (Dipartimento di Matematica, Sapienza Università di Roma, Italy)

Umberto Montemagno (Dipartimento di Matematica, Sapienza Università di Roma, Italy)

Abstract

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.

Keywords

Kuramoto model, complete synchronization, coupled oscillators

2010 Mathematics Subject Classification

74A25, 76N10, 92D25

Full Text (PDF format)

Published 19 August 2015