Synchronizability of multilayer star-ring networks with variable coupling strength

We investigate the synchronizability of multilayer star-ring networks. Two types of multilayer networks, including aggregated coupling and divergent coupling, are established based on the connections between the hub node and the leaf nodes in the subnetwork. The eigenvalue spectrum of the two types of multilayer networks is strictly derived, and the correlation between topological parameters and synchronizability is analyzed by the master stability function framework. Moreover, the variable coupling strength has been investigated, revealing that it is significantly related to the synchronizability of the aggregated coupling while having no influence on the divergent coupling. Furthermore, the validity of the synchronizability analysis is obtained by implementing adaptive control on the multilayer star-ring networks previously mentioned. Calculations and comparisons show that the differences caused by the sizes of multilayer networks and interlayer coupling strength are not negligible. Finally, numerical examples are also provided to validate the effectiveness of the theoretical analysis.