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Neurons in the brain are wired into adaptive networks that exhibit a range ofcollective dynamics. Oscillations, for example, are paradigmatic synchronouspatterns of neural activity with a defined temporal scale. Neuronal avalanches,in contrast, are scale-free cascades of neural activity, often considered asevidence of brain tuning to criticality. While models have been developed toaccount for oscillations or avalanches separately, they typically do notexplain both phenomena, are too complex to analyze analytically, or intractableto infer from data rigorously. Here we propose a non-equilibriumfeedback-driven Ising like class of neural networks that simultaneously andquantitatively captures scale-free avalanches and scale-specific oscillations.In the most simple yet fully microscopic model version we can analyticallycompute the phase diagram and make direct contact with human brainresting-state activity recordings via tractable inference of the model's twoessential parameters. The inferred model quantitatively captures the dynamicsover a broad range of scales, from single sensor oscillations and collectivebehaviors of nearly-synchronous extreme events on multiple sensors, to neuronalavalanches unfolding over multiple sensors across multiple time bins.Importantly, the inferred parameters correlate with model-independentsignatures of "closeness to criticality", indicating that the coexistence ofscale-specific (neural oscillations) and scale-free (neuronal avalanches)dynamics in brain activity occurs close to a non-equilibrium critical point atthe onset of self-sustained oscillations.

Statistical modeling of adaptive neural networks explains coexistence of avalanches and oscillations in resting human brain