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.

翻译：本文探讨了哈密顿动力学对布尔网络交互图的影响。考虑三类动力学：最大高度、哈密顿环以及介于两者之间的中间动力学。研究揭示了这些动力学如何影响图的连通性，以及系统内存在依赖所有其他变量的变量的情况。此外，本文引入了一类能够描述这三种哈密顿行为的单边布尔网络，重点阐明了其特定性质与局限性。研究结果为复杂系统建模提供了理论工具，有助于深化对布尔网络中动态交互机制的理解。