Brain dynamics in an Ising-like class of adaptive neural networks: from oscillations to scaling in collective behaviors

Brain networks exibit a range of collective dynamics and scaling properties. Oscillations, for example, are paradigmatic synchronous patterns of neural activity with a defined temporal scale. Neuronal avalanches, in contrast, are activity cascades in which neuronal groups fire in patterns with no characteristic time or spatial scale. While models have been developed to account for oscillations or avalanches separately, they typically do not explain both phenomena, are too complex to analyze analytically, or intractable to infer from data rigorously. Here we present a non-equilibrium feedback-driven Ising-like class of neural networks that simultaneously and quantitatively captures scale-free avalanches and scale-specific oscillations. In the simplest yet fully microscopic model version we can analytically compute the phase diagram and make direct contact with human brain resting-state activity recordings via tractable inference of the model's two essetial parameters. The inferred model quantitatively captures the dynamics over a broad range of scales, from single sensor oscillations and collective behaviors of nearly-synchronous extreme events on multiple sensors, to neuronal avalanches unfolding over multiple sensors across multiple time bins. Furthermore, the model reproduces distributions and scaling features of coarse-grained resting-state activity, similar to those recently observed in populations of neurons. Importantly, the inferred parameters indicate that the co-existence of scale-specific (oscillations) and scale-free (avalanches) dynamics, as well as the scaling behaviors observed in coarse-grained activity, occurs close to a non-equilibrium critical point at the onset of self-sustained oscillations.