Response of Boolean networks to perturbations

TL;DR

This paper investigates how Boolean networks respond to node perturbations, analyzing return probabilities to attractors through simulations and analytical methods, with applications to evolved and biological networks.

Contribution

It introduces a comprehensive approach combining simulations and analytical results to understand Boolean network robustness and response to perturbations.

Findings

Return probability varies with number of perturbed nodes

Analytical results for Random Boolean Networks

Application to evolved and biological networks

Abstract

We evaluate the probability that a Boolean network returns to an attractor after perturbing h nodes. We find that the return probability as function of h can display a variety of different behaviours, which yields insights into the state-space structure. In addition to performing computer simulations, we derive analytical results for several types of Boolean networks, in particular for Random Boolean Networks. We also apply our method to networks that have been evolved for robustness to small perturbations, and to a biological example.