Dynamical Coarse Graining of Large Scale-Free Boolean networks

TL;DR

This paper introduces a renormalization-like method to analyze large scale-free Boolean networks, revealing universal power-law distributions and self-organized behavior near the edge of chaos, with implications for understanding brain dynamics.

Contribution

The study develops a novel state space coarse-graining approach to uncover universal properties and self-organization in large scale-free Boolean networks.

Findings

State space networks follow universal power-law distributions.

Scale-free Boolean networks exhibit self-organized behavior near chaos.

Power-law behaviors are robust across coarse-graining levels.

Abstract

We present a renormalization-grouplike method performed in the state space for detecting the dynamical behaviors of large scale-free Boolean networks, especially for the chaotic regime as well as the edge of chaos. Numerical simulations with different coarse-graining level show that the state space networks of scale-free Boolean networks follow universal power-law distributions of in and out strength, in and out degree, as well as weight. These interesting results indicate scale-free Boolean networks still possess self-organized mechanism near the edge of chaos in the chaotic regime. The number of state nodes as a function of biased parameter for distinct coarse-graining level also demonstrates that the power-law behaviors are not the artifact of coarse-graining procedure. Our work may also shed some light on the investigation of brain dynamics.