A remote synchronization model of community networks with homogeneous frequencies

In complex nervous systems such as the human brain, the structural and physiological connectivities are only partially correlated, and significant interdependence is observed between the activity of cortical regions that are not directly interconnected. A potential substrate for this decoupling is the phenomenon of remote synchronization, wherein non-adjacent node ensembles become preferentially entrained under suitable conditions. Early studies involving star graphs were grounded on a significant natural frequency mismatch between the hub and leaves. However, this requirement has poor ecological validity, that is, a substantial frequency difference between the hub and leaf nodes is not typically satisfied in biological neural networks. In this study, we propose a community network model comprising one hub community and multiple leaf communities, where all nodes share homogeneous frequencies. A time delay is applied exclusively to the connections associated with the hub community. It is found that the emergence of remote synchronization depends on the coupling strength and time delay matching. Additionally, periodic resonances are observed concerning the natural frequency as well as the time delay. These results are robust across different oscillators and can be accounted for using an equivalent star graph with time delay. By underlining the importance of time delays, a pervasive property of signal propagation in the brain, these results offer a new perspective on the intricate relationship between the configuration of structural couplings and resulting activity synchronization.