Redundancy and error resilience in Boolean Networks

TL;DR

This paper investigates how noise affects sparse Boolean Networks with redundancy, revealing a phase transition from memory-preserving to ergodic behavior and providing bounds on critical noise levels.

Contribution

It demonstrates that redundant Boolean Networks always have a non-zero error level and identifies a phase transition influenced by noise, with bounds on critical noise for various sparsities.

Findings

Networks exhibit a phase transition from non-ergodic to ergodic behavior.

Redundant Boolean Networks always maintain a non-zero error level.

Upper bounds on critical noise levels are derived for different sparsity levels.

Abstract

We consider the effect of noise in sparse Boolean Networks with redundant functions. We show that they always exhibit a non-zero error level, and the dynamics undergoes a phase transition from non-ergodicity to ergodicity, as a function of noise, after which the system is no longer capable of preserving a memory if its initial state. We obtain upper-bounds on the critical value of noise for networks of different sparsity.