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arXiv · 1407.6551

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

Dario Benedetto·Emanuele Caglioti·Umberto Montemagno
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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.

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Dario Benedetto, Emanuele Caglioti, Umberto Montemagno. 2014-07-24. On the complete phase synchronization for the Kuramoto model in the mean-field limit. https://arxiv.org/abs/1407.6551

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