Correlations Induced by Depressing Synapses in Critically Self-Organized Networks with Quenched Dynamics

TL;DR

This paper investigates how depressing synapses affect critical self-organization in neural networks, showing that quenched dynamics induce correlations that alter traditional criticality indicators but still maintain an overall critical state.

Contribution

It demonstrates that quenched synaptic depression leads to correlations affecting branching ratios, yet the network remains critical as indicated by eigenvalue analysis.

Findings

Quenched dynamics cause deviations from branching ratio unity due to correlations.

The network's criticality is confirmed by the largest eigenvalue approaching one.

Finite size effects depend on synaptic parameters.

Abstract

In a recent work, mean-field analysis and computer simulations were employed to analyze critical self-organization in networks of excitable cellular automata where randomly chosen synapses in the network were depressed after each spike (the so-called annealed dynamics). Calculations agree with simulations of the annealed version, showing that the nominal \textit{branching ratio\/} $\sigma$ converges to unity in the thermodynamic limit, as expected of a self-organized critical system. However, the question remains whether the same results apply to the biological case where only the synapses of firing neurons are depressed (the so-called quenched dynamics). We show that simulations of the quenched model yield significant deviations from $\sigma=1$ due to spatial correlations. However, the model is shown to be critical, as the largest eigenvalue of the synaptic matrix approaches unity in the thermodynamic limit, that is, $\lambda_c = 1$ . We also study the finite size effects near the critical state as a function of the parameters of the synaptic dynamics.