Emergence of a Dynamical State of Coherent Bursting with Power-Law Distributed Avalanches from Collective Stochastic Dynamics of Adaptive Neurons

Spontaneous brain activity 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 near a critical point of a phase transition, and attracted much attention. Here, we show that a dynamical 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 consequences of stochasticity and coherent bursting, which in turn is the result of a balance between excitation and adaptation. Our work thus suggests that the observed dynamical features of brain activity can occur in a dynamical regime that emerges from collective stochastic dynamics of adaptive neurons under suitable conditions.