析取布尔网络的动力学性质
Dynamical properties of disjunctive Boolean networks
摘要：
布尔网络是映射$f :\{0,1\}^n \to \{0,1\}^n$，其可用于对$n$交互实体的网络进行建模，每个交互实体具有根据状态的当前配置的确定性函数随时间演变的局部布尔状态。在本文中，我们感兴趣的是析取网络，其中每个局部函数只是一组变量的析取。因此，这个网络是有点同质的，虽然变量的数量可能会因实体而异，从而产生一个广义的元胞自动机。本文的目的是回顾一些主要的结果，得出一些额外的基本结果，并强调一些开放的问题，析取网络的动力学。我们首先回顾了析取网络的不同定义特征，以及使用图、布尔矩阵或二元关系表示它们的几种方法。然后，我们集中在三个动力学性质的析取网络：他们的形象点，他们的周期点，他们的不动点。对于每一类点，我们回顾了如何描述它们的特征，并研究了它们的数量。本文最后与不同的途径，为未来的工作动力学的析取网络，以及如何推广他们。
英文摘要：
A Boolean network is a mapping $f :\{0,1\}^n \to \{0,1\}^n$, which can be used to model networks of $n$ interacting entities, each having a local Boolean state that evolves over time according to a deterministic function of the current configuration of states. In this paper, we are interested in disjunctive networks, where each local function is simply the disjunction of a set of variables. As such, this network is somewhat homogeneous, though the number of variables may vary from entity to entity, thus yielding a generalised cellular automaton. The aim of this paper is to review some of the main results, derive some additional fundamental results, and highlight some open problems, on the dynamics of disjunctive networks. We first review the different defining characteristics of disjunctive networks and several ways of representing them using graphs, Boolean matrices, or binary relations. We then focus on three dynamical properties of disjunctive networks: their image points, their periodic points, and their fixed points. For each class of points, we review how they can be characterised and study how many they could be. The paper finishes with different avenues for future work on the dynamics of disjunctive networks and how to generalise them.
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