Fixed/Predefined Time Intra-Layer Synchronization in Multi-Layer Networks*

This study is dedicated to probing into novel methodologies for attaining predefined-time intra-layer synchronization within multi-layer complex networks. Using particular functions, relatively less stringent conditions are furnished for the predefined time synchronization control strategy. Concurrently, a more accurate estimation of the stabilization time is obtained. Moreover, a specific exploration of synchronization strategies based on the predefined-time approach is carried out. This empowers the synchronization duration to be predetermined in line with practical requisites, independent of system parameters and initial conditions. Eventually, the efficacy of the proposed approach is verified by numerical simulations, thereby proffering novel theoretical foundations and practical guidelines for synchronization management in multi-layer networks.