  Two decades ago, a phenomenon resembling Landau damping was described in the
synchronization of globally coupled oscillators: the evidence of a regime where
the order parameter decays when linear theory predicts neutral stability for
the incoherent state. We here show that such an effect is far more generic, as
soon as phase oscillators couple to their mean field according to their natural
frequencies, being then grouped into two distinct populations of conformists
and contrarians. We report the analytical solution of this latter situation,
which allows determining the critical coupling strength and the stability of
the incoherent state, together with extensive numerical simulations that fully
support all theoretical predictions. The relevance of our results is discussed
in relationship to collective phenomena occurring in polarized social systems.

Chaotic Dynamics