Scaling properties of neuronal avalanches are consistent with critical dynamics

Complex systems, when poised near a critical point of a phase transition between order and disorder, exhibit a dynamics comprising a scale-free mixture of order and disorder which is universal, i.e. system-independent (1-5). It allows systems at criticality to adapt swiftly to environmental changes (i.e., high susceptibility) as well as to flexibly process and store information. These unique properties prompted the conjecture that the brain might operate at criticality (1), a view supported by the recent description of neuronal avalanches in cortex Despite the attractiveness of this idea, its validity is hampered by the fact that its theoretical underpinning relies solely on the replication of sizes and durations of avalanches, which reflect only a portion of the rich dynamics found at criticality. Here we show experimentally five fundamental properties of avalanches consistent with criticality: (1) a separation of time scales, in which the power law probability density of avalanches sizes s, P(s) ~ s α and the lifetime distribution of avalanches are invariant to slow, external driving; (2) stationary P(s) over time; (3) the avalanche probabilities preceding and following main avalanches obey Omori's law (17, 18) for earthquakes; (4) the average size of avalanches following a main avalanche decays as a power law; (5) the spatial spread of avalanches has a fractal dimension and obeys finite-size scaling. Thus, neuronal avalanches are a robust manifestation of criticality in the brain. 2 The spontaneous interaction of hundreds of thousands of neurons in the cerebral cortex gives rise to a bewildering variety of spatio-temporal activity patterns. A fundamental question in neuroscience is to understand the functional meaning of such pattern variety. In that direction, recent work (6-10, 19, 20) has shown that in superficial layers of cortex, spontaneous neuronal activity patterns emerge in the form of " neuronal avalanches ". These are highly diverse bursts of activity exhibiting scale-free features both in space and time. The sizes of avalanches are distributed according to a power-law with an exponent of-3/2 and their durations according to a similar law with an exponent of –2. Avalanches represent a critical balance of excitation and inhibition in the cortex; it is typical that during the course of an avalanche the number of participating neurons neither grows nor substantially decays, such that the branching ratio of the activity stays close to unity, as in other critical systems (21). Neuronal network simulations (11-16) already have replicated quantitatively the observed scale-free …