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

Abstract

In the last decade, several models with network adaptive mechanisms (link deletion-creation, dynamic synapses, dynamic gains) have been proposed as examples of self-organized criticality (SOC) to explain neuronal avalanches. However, all these systems present stochastic oscillations hovering around the critical region that are incompatible with standard SOC. Here we make a linear stability analysis of the mean field fixed points of two self-organized quasi-critical systems: a fully connected network of discrete time stochastic spiking neurons with firing rate adaptation produced by dynamic neuronal gains and an excitable cellular automata with depressing synapses. We find that the fixed point corresponds to a stable focus that loses stability at criticality. We argue that when this focus is close to become indifferent, demographic noise can elicit stochastic oscillations that frequently fall into the absorbing state. This mechanism interrupts the oscillations, producing both power law avalanches and dragon king events, which appear as bands of synchronized firings in raster plots. Our approach differs from standard SOC models in that it predicts the coexistence of these different types of neuronal activity.

Synaptic balance due to homeostatically self-organized quasicritical dynamics

“…Our mean-field calculation is valid for fully connected networks where the number of neighbors is K = N − 1. When there is no threshold θ nor external current I, the condition W = (p − qg)J allows our model to be directly mapped on the Kinouchi et al [16] model.…”

“…Such stochastic oscillations should have low amplitude [16], but rare large events (dragonkings) also occur [15]. Although the demographic noise vanishes in the thermodynamic limit, other sources of biological noise (not included in the model and that does not vanishes for large N ) will continue to trigger the stochastic oscillations and the AI behavior.…”

Modeling neuronal avalanches and long-range temporal correlations at the emergence of collective oscillations: continuously varying exponents mimic M/EEG results

“…This unassuming detail, however, poses a challenge if one wants to explore this class of models to reproduce the above mentioned long-range time correlations which were observed experimentally [17,25]. Since consecutive avalanches are, by definition, separated by returns to the absorbing state, it is not apparent how inter-avalanche correlations could emerge (self-organizing mechanisms are a potential candidate, yet to be tested [15]).…”

Criticality as a measure of developing proteinopathy in engineered human neural networks

“…A more theoretical explanation for the large variability/ fluctuation observed in criticality state, both within and between the neural networks at baseline, can be found within the concept of "dirty criticality". Dirty criticality, or "self-organized quasi criticality", describes a mechanism which drags the activity back and forth around a stretched region of criticality, rather than being defined at a true point of criticality (which is needed to fully comply with standard SoC) (53,(75)(76)(77)(78). This variant might thus contain more plausible models for biological neural networks, as neural network activity actually "hovers" around a region of criticality.…”

“…This variant might thus contain more plausible models for biological neural networks, as neural network activity actually "hovers" around a region of criticality. Here, adaptive criticality (aSoC) models explicitly take into consideration the changing topology of the biological neural networks through dynamic parameters such as synaptic weight alteration, or link deletion and creation, thus encompassing structural network changes and local rewiring rules (75,(77)(78)(79). aSoC is thus based on a co-adaptive process between network architecture and dynamics (56,(80)(81)(82), meaning that the observed fluctuations in network criticality state during the baseline period could result from structural changes occurring in the networks (and vice-versa).…”