The properties of attractors of canalyzing random Boolean networks

TL;DR

This paper analyzes the dynamics of critical canalyzing Boolean networks, revealing how frozen cores form and demonstrating that such networks can have long attractors, with implications for understanding complex system behavior.

Contribution

It introduces a phenomenological theory explaining frozen core formation in canalyzing networks and compares their attractor properties to standard networks.

Findings

Frozen core of nodes arises in canalyzing networks

Canalyzing networks can have very long attractors

Scaling of nonfrozen nodes matches theoretical predictions

Abstract

We study critical random Boolean networks with two inputs per node that contain only canalyzing functions. We present a phenomenological theory that explains how a frozen core of nodes that are frozen on all attractors arises. This theory leads to an intuitive understanding of the system's dynamics as it demonstrates the analogy between standard random Boolean networks and networks with canalyzing functions only. It reproduces correctly the scaling of the number of nonfrozen nodes with system size. We then investigate numerically attractor lengths and numbers, and explain the findings in terms of the properties of relevant components. In particular we show that canalyzing networks can contain very long attractors, albeit they occur less often than in standard networks.