Attractor and Basin Entropies of Random Boolean Networks Under Asynchronous Stochastic Update

TL;DR

This paper introduces a numerical method to analyze the attractor structures and basin entropies of random Boolean networks under asynchronous stochastic update, revealing critical network behaviors and analytical results for specific cases.

Contribution

It presents a novel numerical approach for studying asynchronous Boolean networks and provides analytical insights into attractor and basin size distributions for frozen networks.

Findings

Basin entropy grows with system size only in critical networks.

Distribution of attractor lengths follows a power law in critical networks.

Analytical distribution derived for K=1 frozen networks.

Abstract

We introduce a numerical method to study random Boolean networks with asynchronous stochas- tic update. Each node in the network of states starts with equal occupation probability and this probability distribution then evolves to a steady state. Nodes left with finite occupation probability determine the attractors and the sizes of their basins. As for synchronous update, the basin entropy grows with system size only for critical networks, where the distribution of attractor lengths is a power law. We determine analytically the distribution for the number of attractors and basin sizes for frozen networks with connectivity K = 1.