Influence of a Structure on System's Dynamics on Example of Boolean Networks

TL;DR

This paper investigates how the geometric shape and lattice organization of Boolean Networks influence their dynamics, revealing that structure significantly affects critical behavior and that hierarchy and irregularity promote criticality.

Contribution

It demonstrates the importance of spatial shape and lattice type in the structure-dynamics relation of Boolean Networks, highlighting the role of hierarchy and irregularity in criticality.

Findings

Regular structures do not exhibit critical regimes.

Hierarchy and irregular structures show features of criticality.

Shape and lattice type are crucial for dynamics.

Abstract

In this work we study the Boolean Networks of different geometric shape and lattice organization. It was revealed that no only a spatial shape but also type of lattice are very important for definition of the structure-dynamics relation. The regular structures do not give a critical regime in the investigated cases. Hierarchy together with the irregular structure reveals characteristic features of criticality.