Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, China.
PLoS One. 2013 Jun 13;8(6):e66491. doi: 10.1371/journal.pone.0066491. Print 2013.
A novel algebraic approach is proposed to study dynamics of asynchronous random Boolean networks where a random number of nodes can be updated at each time step (ARBNs). In this article, the logical equations of ARBNs are converted into the discrete-time linear representation and dynamical behaviors of systems are investigated. We provide a general formula of network transition matrices of ARBNs as well as a necessary and sufficient algebraic criterion to determine whether a group of given states compose an attractor of length[Formula: see text] in ARBNs. Consequently, algorithms are achieved to find all of the attractors and basins in ARBNs. Examples are showed to demonstrate the feasibility of the proposed scheme.
本文提出了一种新的代数方法来研究异步随机布尔网络（ARBN）的动力学，其中每个时间步可以更新任意数量的节点。在本文中，将 ARBN 的逻辑方程转换为离散时间线性表示，并研究了系统的动态行为。我们给出了 ARBN 网络转移矩阵的一般公式，以及确定给定状态组是否构成 ARBN 中长度为[Formula: see text]的吸引子的必要和充分的代数准则。因此，得到了在 ARBN 中寻找所有吸引子和吸引域的算法。通过示例验证了所提出方案的可行性。
