Emergence of a dynamical state of coherent bursting with power-law distributed avalanches from collective stochastic dynamics of adaptive neurons

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.