Can dynamical synapses produce true self-organized criticality?

TL;DR

This paper demonstrates that a network of excitable cellular automata with dynamical synapses can exhibit true self-organized criticality, aligning with conservative SOC models, even with dissipative dynamics, due to average conservation in the stationary state.

Contribution

It shows that dynamical synapses can produce true SOC behavior, expanding understanding of criticality in neuronal network models beyond quasi-criticality.

Findings

Model exhibits power-law avalanches similar to critical systems.

Stationary regime is conservative on average, leading to true SOC.

Analytical results match simulations and explain SOC emergence.

Abstract

Neuronal networks can present activity described by power-law distributed avalanches presumed to be a signature of a critical state. Here we study a random-neighbor network of excitable cellular automata coupled by dynamical synapses. The model exhibits a very similar to conservative self-organized criticality (SOC) models behavior even with dissipative bulk dynamics. This occurs because in the stationary regime the model is conservative on average, and, in the thermodynamic limit, the probability distribution for the global branching ratio converges to a delta-function centered at its critical value. So, this non-conservative model pertain to the same universality class of conservative SOC models and contrasts with other dynamical synapses models that present only self-organized quasi-criticality (SOqC). Analytical results show very good agreement with simulations of the model and enable us to study the emergence of SOC as a function of the parametric derivatives of the stationary branching ratio.