Emergence of power-law distributed avalanches from stochastic dynamics of adaptive neurons in a network when there is a balance between excitation and adaptation

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 observations have been interpreted as evidence supporting the hypothesis that the brain is operating near a critical point between two states and attracted much attention. Using numerical simulations of networks of adaptive neurons with stochastic input, we find that a state of coherent bursting emerges when excitation is sufficiently strong and balanced by adaptation, and avalanches with power-law size and duration distributions occur in this state. When excitation is too weak, neurons exhibit irregular and independent spiking and when excitation is too strong for the adaptation, neurons exhibit incoherent fast spiking and in these two states, durations of the avalanches are exponentially distributed. We demonstrate that the power-law distributed avalanches are direct consequences of stochasticity and coherent bursting, which is in turn the result of a balance between excitation and adaptation. Our work thus shows that power-law distributed avalanches can arise from collective stochastic dynamics of adaptive neurons when there is a balance between excitation and adaptation and need not be signatures of criticality.