Phase Transitions in Random Boolean Networks with Different Updating Schemes

TL;DR

This study investigates how different updating schemes in Random Boolean networks influence their phase transitions, revealing that the critical connectivity threshold is similar across schemes and depends mainly on network size.

Contribution

It provides a comprehensive comparison of phase transitions across various updating schemes in Random Boolean networks using computer simulations.

Findings

All network types exhibit phase transitions when average connections are between one and three.

The critical connectivity value is largely independent of the updating scheme.

Network size influences the phase transition point more than the updating scheme.

Abstract

In this paper we study the phase transitions of different types of Random Boolean networks. These differ in their updating scheme: synchronous, semi-synchronous, or asynchronous, and deterministic or non-deterministic. It has been shown that the statistical properties of Random Boolean networks change considerable according to the updating scheme. We study with computer simulations sensitivity to initial conditions as a measure of order/chaos. We find that independently of their updating scheme, all network types have very similar phase transitions, namely when the average number of connections of nodes is between one and three. This critical value depends more on the size of the network than on the updating scheme.