This article is set in the field of regulation networks modeled by discrete dynamical systems. It focuses on Boolean automata networks. In such networks, there are many ways to update the states of every element. When this is done deterministically, at each time step of a discretised time flow and according to a predefined order, we say that the network is updated according to block-sequential update schedule (blocks of elements are updated sequentially while, within each block, the elements are updated synchronously). Many studies, for the sake of simplicity and with some biologically motivated reasons, have concentrated on networks updated with one particular block-sequential update schedule (more often the synchronous/parallel update schedule or the sequential update schedules). The aim of this paper is to give an argument formally proven and inspired by biological considerations in favour of the fact that the choice of a particular update schedule does not matter so much in terms of the possible and likely dynamical behaviours that networks may display.
自动机网络是f：Q Z $\rightarrow$ Q Z形式的映射，其中Q是有限字母表，Z是实体的集合;它们推广了元胞自动机和布尔网络。更新调度规定每个实体何时根据其本地函数fi更新其状态：Q Z $\rightarrow$ Q。一个主要的问题是研究一个给定的自动机网络在不同的更新时间表下的行为。在本文中，我们研究了自动机网络，在许多不同的更新计划下是不变的。这就产生了两个定义，局部交换网络和全局交换网络。我们研究了交换性和更新函数的不同形式的局部性之间的关系;一个主要结论是全局交换网络具有很强的动力学性质，而局部交换网络的约束要少得多。我们还给出了所有全局交换布尔网络的一个完整分类。
CANA: A python package for quantifying control and canalization in Boolean Networks
School of Informatics, Computing, and Engineering Indiana University（印第安纳大学信息学、计算与工程学院）；CAPES Foundation, Ministry of Education of Brazil（巴西教育部CAPAS基金会）；Center for Complex Networks Research, Northeastern University（东北大学复杂网络研究中心）
