Synchronization of periodically time-varying Boolean networks under state-flipping control

This paper investigates the synchronization of a drive-response system formed by coupling two periodically time-varying Boolean networks (PTVBNs) under state-flipping control. Both synchronous and asynchronous update PTVBNs are taken into consideration. First, sufficient and necessary conditions for synchronization are proposed. Second, two algorithms are provided to find the flip sequence with minimum cardinality, enabling the response system to track the state trajectory of the drive system based on synchronous and asynchronous update schemes. However, the obtained flip sequence is only applicable to the given initial states. Therefore, another algorithm is presented to find the minimum flip set, which is suitable for all initial states. Finally, an example is given to illustrate the effectiveness of the obtained results.