Synchronizability of multilayer totally homogeneous networks

In this study, we concentrate on the synchronizability of multilayer totally homogeneous networks. The eigenvalue spectrum of four typical multilayer networks, including multilayer nearest-neighbor regular networks, multilayer small-world networks, multilayer random networks and multilayer totally homogeneous networks, has been rigorously derived and the synchronizability of four typical multilayer networks has been compared due to the master stability function. Furthermore, numerical simulations are performed to validate the synchronizability of these multilayer networks. The results indicate that multilayer totally homogeneous networks exhibit optimal synchronizability. The Euler characteristic numbers and Betti numbers of these networks are derived, and their relationships with the synchronizability of multilayer networks are analyzed. We can observe that a negative correlation is exhibited between the Euler characteristic number and the synchronizability of multilayer networks, while a positive correlation is exhibited between the Betti number and the synchronizability of multilayer networks.