Synchronization and dephasing results for the Kuramoto model

The Kuramoto model, a deterministic model describes a large population of coupled oscillators with natural frequencies drawn from some prescribed distribution. In the thesis are presented the results obtained in collaboration with Dario Benedetto and Emanuele Caglioti about synchronization and dephasing. In particular it is shown that, in the case of identical oscillators, the phase-synchronization is the 'typical' behavior. In the small coupling regime, it is proved the dephasing of the oscillators by using the decaying of the order parameter. The techniques used in this second part take inspiration from the literature on the Landau Damping.