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In the last decade, several models with network adaptive mechanisms (linkdeletion-creation, dynamic synapses, dynamic gains) have been proposed asexamples of self-organized criticality (SOC) to explain neuronal avalanches.However, all these systems present stochastic oscillations hovering around thecritical region that are incompatible with standard SOC. This phenomenology hasbeen called self-organized quasi-criticality (SOqC). Here we make a linearstability analysis of the mean field fixed points of two SOqC systems: a fullyconnected network of discrete time stochastic spiking neurons with firing rateadaptation produced by dynamic neuronal gains and an excitable cellularautomata with depressing synapses. We find that the fixed point corresponds toa stable focus that loses stability at criticality. We argue that when thisfocus is close to become indifferent, demographic noise can elicit stochasticoscillations that frequently fall into the absorbing state. This mechanisminterrupts the oscillations, producing both power law avalanches and dragonking events, which appear as bands of synchronized firings in raster plots. Ourapproach differs from standard SOC models in that it predicts the coexistenceof these different types of neuronal activity.

Stochastic oscillations produce dragon king avalanches in self-organized quasi-critical systems