  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.
