  Oscillators coupled in a network can synchronize with each other to yield a
coherent population rhythm. If multiple such networks are coupled together, the
question arises whether these rhythms will synchronize. We investigate the
impact of noise on this synchronization for strong inhibitory pulse-coupling
and find that increasing the noise can synchronize the population rhythms, even
if the noisy inputs to different oscillators are completely uncorrelated.
Reducing the system to a phenomenological iterated map we show that this
synchronization of the rhythms arises from the noise-induced phase
heterogeneity of the oscillators. The synchronization of population rhythms is
expected to be particularly relevant for brain rhythms.
