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Synchronization of Interconnected Multi‐valued Logical Networks
Author(s) -
Meng Min,
Feng June,
Hou Zhongsheng
Publication year - 2014
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.835
Subject(s) - synchronization (alternating current) , set (abstract data type) , synchronization networks , boolean network , computer science , logical conjunction , mathematics , algebraic number , topology (electrical circuits) , theoretical computer science , discrete mathematics , boolean function , combinatorics , mathematical analysis , programming language
This paper studies the synchronization of interconnected k ‐valued logical networks, as well as that of interconnected higher order k ‐valued logical networks, based on their algebraic representations. For interconnected k ‐valued logical networks, one necessary and sufficient criterion of synchronization is established via the definition of synchronization and another equivalent condition is given by combining synchronization with fixed points and cycles. Furthermore, with some special properties of semi‐tensor product, the third necessary and sufficient condition for synchronization of interconnected k ‐valued logical networks is raised in terms of transition matrices. Then, the limit set method can be used to analyze the synchronization of interconnected higher order k ‐valued logical networks. Finally, three examples, including the Boolean model for interconnected biochemical oscillators in the cell cycle, are presented to illustrate effectiveness of the results.