Hamiltonian dynamics of Boolean networks

TL;DR

This paper explores how Hamiltonian dynamics affect the structure and behavior of Boolean networks, introducing a family of networks that exhibit these dynamics and analyzing their properties.

Contribution

It introduces a family of unate Boolean networks capable of modeling Hamiltonian dynamics and provides theoretical insights into their structural properties.

Findings

Hamiltonian dynamics influence the connectivity of Boolean network graphs.

Existence of variables dependent on all others varies with dynamics type.

Theoretical tools are developed for modeling complex systems with these dynamics.

Abstract

This article examines the impact of Hamiltonian dynamics on the interaction graph of Boolean networks. Three types of dynamics are considered: maximum height, Hamiltonian cycle, and an intermediate dynamic between these two. The study addresses how these dynamics influence the connectivity of the graph and the existence of variables that depend on all other variables in the system. Additionally, a family of unate Boolean networks capable of describing these three Hamiltonian behaviors is introduced, highlighting their specific properties and limitations. The results provide theoretical tools for modeling complex systems and contribute to the understanding of dynamic interactions in Boolean networks.