Synchronization and frustration in oscillator networks with attractive and repulsive interactions

We study, numerically and analytically, the stability of synchronization for an ensemble of coupled phase oscillators with attractive and repulsive interactions, as a function of the number of repulsive couplings and their intensity. Scaling properties of the desynchronization transition are disclosed, and it is shown that unsynchronized configurations have different symmetries depending on the intensity of the repulsive interaction. The concept of frustration minimization helps understanding the main features observed in the collective dynamics of the oscillator network.