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| Recently, there have been considerable interests in the study of spontaneous synchronization, particularly within the framework of the Kuramoto model. The model comprises oscillators with distributed natural frequencies interacting through a mean-field coupling, and serves as a paradigm to study synchronization. In this talk, I will outline recent progress. In particular, I put forward a general framework in which I wll discuss in a unified way known results with more recent developments obtained for a generalized Kuramoto model that includes inertial effects and noise. I describe the model from a different perspective, emphasizing the equilibrium and out-of-equilibrium aspects of its dynamics from a statistical physics point of view: i) I discuss the phase diagram for unimodal frequency distributions; ii) I analyze the dynamics on a lattice where the coupling decays algebraically with separation between lattice sites, and discuss for specific cases how the long-time transition to synchrony is essentially governed by the dynamics of the mean-field mode. |
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