IEEE Trans Neural Netw Learn Syst. 2018 Apr;29(4):819-831. doi: 10.1109/TNNLS.2017.2647989. Epub 2017 Jan 24.
This paper investigates the synchronization problem for the realization-dependent probabilistic Boolean networks (PBNs) coupled unidirectionally in the drive-response configuration. The realization of the response PBN is assumed to be uniquely determined by the realization signal generated by the drive PBN at each discrete time instant. First, the drive-response PBNs are expressed in their algebraic forms based on the semitensor product method, and then, a necessary and sufficient condition is presented for the synchronization of the PBNs. Second, by resorting to a newly defined matrix operator, the reachable set from any initial state is expressed by a column vector. Consequently, an easily computable algebraic criterion is derived assuring the synchronization of the drive-response PBNs. Finally, three illustrative examples are employed to demonstrate the applicability and usefulness of the developed theoretical results.
本文研究了在驱动-响应配置下单向耦合的实现依赖概率布尔网络（PBN）的同步问题。假设响应 PBN 的实现是由驱动 PBN 在每个离散时间点产生的实现信号唯一确定的。首先，基于半张量积方法将驱动-响应 PBN 表示为其代数形式，然后给出了 PBN 同步的充分必要条件。其次，通过引入一个新定义的矩阵算子，将从任意初始状态可达的集合表示为一个列向量。因此，得出了一个易于计算的代数判据，以确保驱动-响应 PBN 的同步。最后，通过三个实例验证了所提出理论结果的有效性和实用性。
