  Spontaneous brain activity in the absence of external stimuli is not random
but contains complex dynamical structures such as neuronal avalanches with
power-law duration and size distributions. These experimental observations have
been interpreted as supporting evidence for the hypothesis that the brain is
operating at criticality and attracted much attention. Here, we show that an
entire state of coherent bursting, with power-law distributed avalanches and
features as observed in experiments, emerges in networks of adaptive neurons
with stochastic input when excitation is sufficiently strong and balanced by
adaptation. We demonstrate that these power-law distributed avalanches are
direct consequences of stochasticity and the oscillatory population firing rate
arising from coherent bursting, which in turn is the result of the balance
between excitation and adaptation, and criticality does not play a role.
