Synchronisation analysis of Boolean networks based on equivalence

This study studies the synchronisation of two Boolean networks (BNs) coupled in the drive-response configuration, and presents a number of new results. A new indicator variable, which plays an important role in characterising the synchronised nodes between the drive BN and the response BN, is defined by coordinate equivalence. Consequently, some necessary and sufficient conditions are derived for the general synchronisation of the drive-response BNs. Moreover, the upper bound of time to check the criterion is given. Two examples are provided to illustrate the efficiency of the obtained results.