  We discuss the desynchronization transition in networks of globally coupled
identical oscillators with attractive and repulsive interactions. We show that,
if attractive and repulsive groups act in antiphase or close to that, a
solitary state emerges with a single repulsive oscillator split up from the
others fully synchronized. With further increase of the repulsing strength, the
synchronized cluster becomes fuzzy and the dynamics is given by a variety of
stationary states with zero common forcing. Intriguingly, solitary states
represent the natural link between coherence and incoherence. The phenomenon is
described analytically for phase oscillators with sine coupling and
demonstrated numerically for more general amplitude models.
