Formation of the frozen core in critical Boolean Networks

TL;DR

This paper studies how the frozen core forms in critical Boolean networks, revealing limitations of existing algorithms and providing new simulation and analytical insights into the process.

Contribution

It introduces a mean-field approach to analyze frozen core formation and identifies the failure of previous algorithms for nodes with more than four inputs.

Findings

Efficient algorithms fail beyond 4 inputs per node.

Mean-field calculations accurately predict frozen core features.

Simulation data confirms analytical predictions.

Abstract

We investigate numerically and analytically the formation of the frozen core in critical random Boolean networks with biased functions. We demonstrate that a previously used efficient algorithm for obtaining the frozen core, which starts from the nodes with constant functions, fails when the number of inputs per node exceeds 4. We present computer simulation data for the process of formation of the frozen core and its robustness, and we show that several important features of the data can be derived by using a mean-field calculation.