Synchronization of Arbitrarily Switched Boolean Networks

• Published in: IEEE transaction on neural networks and learning systems Vol. 28; no. 3; pp. 612 - 619
• Main Authors: Chen, Hongwei, Liang, Jinling, Huang, Tingwen, Cao, Jinde
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.03.2017; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algebra; Biology; Boolean algebra; Boolean functions; Complete synchronization; Controllability; semitensor product (STP); switched Boolean networks (SBNs); Switches; switching reachable set; Switching theory; Synchronism; Synchronization; Yttrium
• ISSN: 2162-237X; 2162-2388
• DOI: 10.1109/TNNLS.2015.2497708

This paper investigates the complete synchronization problem for the drive-response switched Boolean networks (SBNs) under arbitrary switching signals, where the switching signals of the response SBN follow those generated by the drive SBN at each time instant. First, the definition of complete synchronization is introduced for the drive-response SBNs under arbitrary switching signals. Second, the concept of switching reachable set starting from a given initial state set is put forward. Based on it, a necessary and sufficient condition is derived for the complete synchronization of the drive-response SBNs. Last, we give a simple algebraic expression for the switching reachable set in a given number of time steps, and two computable algebraic criteria are obtained for the complete synchronization of the SBNs. A biological example is given to demonstrate the effectiveness of the obtained main results.