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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Benedetto et al. (2015) studied this question.
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