Hamiltonian dynamics of Boolean networks
Theoretical contribution for researchers studying Boolean networks and complex systems, but incremental as it extends known dynamics to a specific network family.
The paper studies how Hamiltonian dynamics (maximum height, Hamiltonian cycle, and an intermediate) affect the interaction graph of Boolean networks, introducing a family of unate networks that can exhibit these behaviors. It provides theoretical tools for modeling complex systems.
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.