Canalizing Kauffman networks: non-ergodicity and its effect on their critical behavior

TL;DR

This paper introduces a method to determine the critical behavior of Boolean networks, specifically those with canalizing functions, and provides evidence for its accuracy in predicting phase transitions from order to chaos.

Contribution

The authors develop a general approach to analyze the critical behavior of Boolean networks with arbitrary ensembles of functions, focusing on canalizing functions, and validate it with numerical evidence.

Findings

Successfully predicts phase transition points in canalizing Boolean networks

Provides a general method applicable to various Boolean function ensembles

Numerical results confirm the accuracy of the theoretical predictions

Abstract

Boolean Networks have been used to study numerous phenomena, including gene regulation, neural networks, social interactions, and biological evolution. Here, we propose a general method for determining the critical behavior of Boolean systems built from arbitrary ensembles of Boolean functions. In particular, we solve the critical condition for systems of units operating according to canalizing functions and present strong numerical evidence that our approach correctly predicts the phase transition from order to chaos in such systems.