On the length of attractors in boolean networks with an interaction graph by layers

TL;DR

This paper establishes an upper bound on the length of attractors in boolean networks with acyclic interaction graphs, linking the network's dynamic behavior to its structural properties.

Contribution

It introduces a novel upper bound on attractor lengths for boolean networks with interaction graphs lacking circuits longer than one, based solely on the graph structure.

Findings

Upper bound on attractor length depends only on the interaction graph

Networks without long circuits have limited attractor lengths

Structural properties constrain dynamic complexity

Abstract

We consider a boolean network whose interaction graph has no circuit of length >1. Under this hypothesis, we establish an upper bound on the length of the attractors of the network which only depends on its interaction graph.