Bridge links induced remote synchronization in multiple connected star graphs

Remote synchronization (RS) is currently a hot topic in the fields of nonlinear dynamics and complex networks, aiming to understand how the distant connections of brain functional network come from its brain structural network. So far, most studies of RS assume the same coupling for all nodes. However, a brain network consists of communities and rich-club where their nodes take different roles. To study their influence to RS, herein we present a model of multiple connected star graphs where the bridge nodes are assumed to represent the rich-club and thus their links are assumed to have different couplings from the non-bridge links. We find that this setup of couplings will seriously influence RS and results in two new phases: (i) the leaf nodes are synchronized each other but they do not synchronize with either the bridge or hub nodes; and (ii) both the leaf and hub nodes are synchronized each other but they do not synchronize with the bridge nodes, i.e. the bridge nodes take the role of new hubs while the hubs become part of leaf nodes, thus named as bridge induced RS. This finding clarifies a misunderstanding in previous studies that RS can be only induced by the hub of star graph and makes us realize that RS is in fact induced by the node taking the role of relay node, no matter it is the hub, bridge, or other node. Further, we show that the bridge induced RS exists for both symmetric and asymmetric couplings of bridge links and can be extended to the case of multiple connected star graphs, thus providing new insights to understand the distant connections of brain functional networks. Finally, a brief theoretical analysis is provided to explain these results.