Perturbation propagation in random and evolved Boolean networks

TL;DR

This paper studies how perturbations spread in Boolean networks, revealing that evolved networks exhibit mixed dynamical behaviors and challenging traditional classifications, with implications for understanding network robustness.

Contribution

It demonstrates that evolved Boolean networks do not fit traditional categories and shows how their state space properties influence perturbation propagation.

Findings

Random Boolean networks align with annealed approximation predictions.

Evolved networks display properties of frozen, critical, and chaotic networks.

Modified Derrida plots reflect specific state space characteristics.

Abstract

We investigate the propagation of perturbations in Boolean networks by evaluating the Derrida plot and modifications of it. We show that even small Random Boolean Networks agree well with the predictions of the annealed approximation, but non-random networks show a very different behaviour. We focus on networks that were evolved for high dynamical robustness. The most important conclusion is that the simple distinction between frozen, critical and chaotic networks is no longer useful, since such evolved networks can display properties of all three types of networks. Furthermore, we evaluate a simplified empirical network and show how its specific state space properties are reflected in the modified Derrida plots.