Remote synchronization in multi-layered community networks with star-like topology

Remote synchronization (RS) is currently a hot topic in the fields of nonlinear science and complex network and has a close relationship with signal propagation in brain networks. So far, most studies of RS are focused on star graphs. However, realistic networks with RS are much more complicated than a purely star graph, such as various cognitive networks in human brain. Thus, we here present a model of multi-layered community network to extend the study of RS from star graphs to star-like community topologies, i.e. each node of star graph becoming a community. We find that RS may appear in this multi-layered network model, provided that the hub community has a stronger coupling while the leaf communities have a weaker coupling. A measure of RS is introduced to investigate the influence of key parameters such as the frequency distributions, network size, and natural frequency difference between the hub and leaf layers. Moreover, these results have been confirmed in the sub-networks from a real brain network. And a brief theoretical analysis is provided to explain the mechanism of RS in multi-layered community networks.