Synchronization Analysis and Design of Coupled Boolean Networks Based on Periodic Switching Sequences

A novel synchronization analysis method is developed to solve the complete synchronization problem of many Boolean networks (BNs) coupled in the leader-follower configuration. First, an error system is constructed in terms of the algebraic representation using the semitensor product of matrices. Then, the synchronization problem of coupled BNs is converted into a problem whether all the trajectories of the error system are convergent to the zero vector. Second, according to the structure analysis of this error system, which is in the form of a switched system with leader BN states as the switching signal, a necessary and sufficient synchronization condition is derived. An algorithm is developed, which helps to determine as soon as possible whether complete synchronization among coupled BNs is achieved. Finally, a constructive design approach to follower BNs is provided. All of these follower BNs designed by our approach can completely synchronize with a given leader BN from the (T-t + 1)th step at most, where T-t is the transient period of the leader BN.