Approximate synchronization of coupled multi-valued logical networks.

This article addresses the approximate synchronization problem of two coupled multi-valued logical networks, including global and local cases. Three new notions: approximate synchronization state set (ASSS), the maximum approximate synchronization basin (MASB) and the shortest approximate synchronization time (SAST) are introduced and analyzed. Based on ASSS, several necessary and sufficient conditions are obtained for global and local approximate synchronization. MASB, the set of all possible initial states from which the systems are approximately synchronous, is investigated combining with the maximum invariant subset. Meanwhile, the calculation method of the SAST, associated with the transient period, is presented. By virtue of MASB and SAST, pinning controllers are designed to make the coupled systems achieve global approximate synchronization. Furthermore, the PSPACE-completeness of the approximate synchronization problem is proved. Finally, several examples are given to illustrate the obtained results. [ABSTRACT FROM AUTHOR]