Partial Synchronization of Interconnected Boolean Networks
研究了互联布尔网络的部分同步问题，利用矩阵半张量积给出充要判据，并通过诱导有向图建立等价图形描述，最后用两个例子（包括表观遗传模型）验证结果。
This paper addresses the partial synchronization problem for the interconnected Boolean networks (BNs) via the semi-tensor product (STP) of matrices. First, based on an algebraic state space representation of BNs, a necessary and sufficient criterion is presented to ensure the partial synchronization of the interconnected BNs. Second, by defining an induced digraph of the partial synchronized states set, an equivalent graphical description for the partial synchronization of the interconnected BNs is established. Consequently, the second partial synchronization criterion is derived in terms of adjacency matrix of the induced digraph. Finally, two examples (including an epigenetic model) are provided to illustrate the efficiency of the obtained results.