Synchronization of interconnected multi-valued logical networks

This paper studies the synchronization between two interconnected k-valued logical networks based on their algebraic representations. First, one necessary and sufficient criterion of synchronization is established via the definition of synchronization. Then another equivalent condition of synchronization is given combining synchronization with fixed points and limit cycles. Furthermore, with some special properties of semi-tensor product, the third necessary and sufficient condition is raised in terms of transition matrices. At last, the examples are presented to illustrate effectiveness of the results.