  We develop a theory for the emergence of global firings in non-identical
excitable systems subject to noise. Three different dynamical regimes arise:
sub-threshold motion, where all elements remain confined near the fixed point;
coherent pulsations, where a macroscopic fraction fire simultaneously; and
incoherent pulsations, where units fire in a disordered fashion. We also show
that the mechanism for global firing is generic: it arises from degradation of
entrainment originated either by noise or by diversity.
