A state-flipped approach to complete synchronization of Boolean networks

State flipping is an effective control method that has just recently been proposed. In this paper, the state-flipped mechanism is introduced to implement the complete synchronization problem of BNs by use of the semi-tensor product (STP) of matrices. Firstly, an algebraic expression of BNs with state-flipped mechanism is constructed, and under such representation, the validation conditions for the existence of the complete synchronization of drive-response BNs are derived. Subsequently, the synchronization results with state-flipped control of the above system is further extended to more general BNs by analyzing the synchronous flip sequence. Meanwhile, some algorithms are developed to find and determine the corresponding sequence of synchronous flips and the set of minimum synchronous flips. Finally, several typical numerical examples are offered in detail to demonstrate the validity of obtained results. To sum up, the current research may further enrich and develop the study of network synchronization problem.