Synchronization of Coupled Boolean Networks With Different Update Scheme

In this paper, the synchronization of coupled Boolean networks with asynchronous update scheme is investigated. First, the asynchronous Boolean dynamics is transformed into a linear expression with the semi-tensor product technique. Then, the synchronization cycle is proposed to establish the synchronization conditions of asynchronous Boolean networks. Furthermore, an algorithm is given, which can be used to quickly check whether there exists the synchronization cycle in the coefficient matrix of the Boolean function. Finally, an example is provided to verify the efficiency of the theoretical analysis.