Synchronization analysis for Asynchronous k-valued logical Networks

In this paper, the synchronization problems of k-valued logical networks are investigated under asynchronous update strategy. First, we study the inner synchronization of asynchronous k-valued logical networks, then, based on the algebraic representations of asynchronous k-valued logical networks with the semi-tenor product of matrices, establish a necessary and sufficient criterion on the inner synchronization of asynchronous k-valued logical networks. Next, we investigate the outer synchronization between a driving asynchronous k-valued logical network and a corresponding response k-valued logical network, and give a theorem for outer synchronization of asynchronous k-valued logical networks. Finally, two illustrative examples are provided to verify the efficiency of the proposed results.