Boolean finite dynamical systems (FDS) are commonly used in systems biology to model the dynamics of intracellular regulatory networks and interpret the emergence of cellular behaviors. Given a Boolean FDS, we can compute the corresponding regulatory network, that is a directed signed graph representing all the interactions between components (genes), endowed with logical rules specifying the dynamical behavior of the system. We consider the asynchronous trajectories generated by this Boolean FDS, supported by the hypercube. The exploration and analysis of this dynamics is a challenging task because of the combinatorial explosion that we face. A way to approach this problem is to exploit the links between the regulatory graph and the dynamics.

We use the isometries of the hypercube to define classes gathering all the isometric Boolean FDS. Thus, we classify the set of Boolean FDS on the basis of those isometries, and emphasize their common features through regulatory graphs and logical rules. We can then restrict the dynamical analysis of all the Boolean FDS to one representative per class, and thereby considerably improve the efficiency of analysis of all the Boolean FDS. Relying on invariants properties, we propose a constructive method to provide, given a FDS, a representative regulatory graph of its class.

We illustrate the efficiency of the method in concrete situations. For instance, the motif analysis (Remy et al., 2003; Remy et al., 2016; Didier and Remy, 2012) is strongly improved thanks to this classification. We also revisit the negative Thomas’ rule (Remy and Ruet, 2008; Richard, 2010) by establishing a new demonstration.

布尔有限动力系统（FDS）通常用于系统生物学中，以模拟细胞内调控网络的动力学并解释细胞行为的出现。给定布尔FDS，我们可以计算相应的监管网络，即表示组件（基因）之间所有交互的有向图，并带有指定系统动态行为的逻辑规则。我们考虑由超立方体支持的此布尔FDS生成的异步轨迹。由于我们面临着组合爆炸，因此对这种动力学的探索和分析是一项具有挑战性的任务。解决此问题的一种方法是利用调节图和动力学之间的联系。

我们使用超立方体的等轴测图来定义收集所有等距布尔FDS的类。因此，我们根据这些等距对布尔FDS集进行分类，并通过监管图和逻辑规则强调它们的共同特征。然后，我们可以将所有布尔FDS的动态分析限制为每类一个代表，从而大大提高了所有布尔FDS的分析效率。依靠不变性的性质，我们提出了一种建设性的方法，以给定FDS来提供其类别的代表性监管图。

我们说明了该方法在具体情况下的有效性。例如，由于这种分类，主题分析（Remy等人，2003； Remy等人，2016； Didier and Remy，2012）得到了极大的改进。我们还通过建立新的示威活动，重新审视了托马斯的消极法则（Remy and Ruet，2008； Richard，2010）。