Collective dynamics of coupled oscillators

Antonio Politi
University of Aberdeen

In the last years the evolution of coupled nonlinear oscillators has attracted an increasing interest for the several freaky regimes that may emerge even when the single units are simple phase oscillators. I will pay a special attention to collective properties, where, by "collective" I mean the spontaneous emergence of macroscopic features, such as the synchronization testified by a nonzero Kuramoto order parameter and accompanied by a nontrivial dynamics. The role of heterogeneity, coupling function, amplitude fluctuations, competition between excitation and inhibition, and coupling sparseness will be reviewed illustrating the various regimes that have been so far identified.