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This article deals with the approximate synchronization of two coupledmulti-valued logical networks. According to the initial state set from whichboth systems start, two kinds of approximate synchronization problem, localapproximate synchronization and global approximate synchronization, areproposed for the first time. Three new notions: approximate synchronizationstate set (ASSS), the maximum approximate synchronization basin (MASB) and theshortest approximate synchronization time (SAST) are introduced and analyzed.Based on ASSS, several necessary and sufficient conditions are obtained forapproximate synchronization. MASB, the set of all possible initial states, fromwhich the systems are approximately synchronous, is investigated combining withthe maximum invariant subset. And the calculation method of the SAST,associated with transient period, is presented. By virtue of MASB, pinningcontrol scheme is investigated to make two coupled systems achieve globalapproximate synchronization. Furthermore, the related theories are also appliedto the complete synchronization problem of $k$-valued ($k\geq2$) logicalnetworks. Finally, four examples are given to illustrate the obtained results.

Approximate synchronization of coupled multi-valued logical networks