Analytical investigation of self-organized criticality in neural networks

TL;DR

This paper models neural networks as adaptive systems with activity-dependent rewiring, demonstrating analytically and numerically how they self-organize into a critical state that enhances information processing.

Contribution

It introduces a stochastic discrete-state neuron model with plasticity rules that analytically and numerically show self-organization to criticality in neural networks.

Findings

System undergoes a phase transition at a critical connectivity.

Activity-dependent rewiring leads to stable critical states.

Model demonstrates self-organized criticality through bifurcation analysis.

Abstract

Dynamical criticality has been shown to enhance information processing in dynamical systems, and there is evidence for self-organized criticality in neural networks. A plausible mechanism for such self-organization is activity dependent synaptic plasticity. Here, we model neurons as discrete-state nodes on an adaptive network following stochastic dynamics. At a threshold connectivity, this system undergoes a dynamical phase transition at which persistent activity sets in. In a low dimensional representation of the macroscopic dynamics, this corresponds to a transcritical bifurcation. We show analytically that adding activity dependent rewiring rules, inspired by homeostatic plasticity, leads to the emergence of an attractive steady state at criticality and present numerical evidence for the system's evolution to such a state.