Stability of Boolean Multilevel Networks

TL;DR

This paper investigates how multilevel structures in Boolean Networks can stabilize overall system dynamics, even when individual layers are chaotic, highlighting new feedback mechanisms and control possibilities.

Contribution

It introduces a semi-annealed approximation to analyze stability in multiplex Boolean Networks, revealing how interlayer coupling stabilizes chaotic layers.

Findings

Multilevel structure stabilizes chaotic Boolean Network layers.

Coupling modifies phase diagrams and critical conditions.

Interdependency can serve as a control mechanism.

Abstract

The study of the interplay between the structure and dynamics of complex multilevel systems is a pressing challenge nowadays. In this paper, we use a semi-annealed approximation to study the stability properties of Random Boolean Networks in multiplex (multi-layered) graphs. Our main finding is that the multilevel structure provides a mechanism for the stabilization of the dynamics of the whole system even when individual layers work on the chaotic regime, therefore identifying new ways of feedback between the structure and the dynamics of these systems. Our results point out the need for a conceptual transition from the physics of single layered networks to the physics of multiplex networks. Finally, the fact that the coupling modifies the phase diagram and the critical conditions of the isolated layers suggests that interdependency can be used as a control mechanism.