Remote propagation of external signals

Recent studies in nonlinear dynamics and complex networks have significantly advanced our understanding of brain functions, particularly in areas such as chimera states, remote synchronization, and remote firing propagation. However, how external signals propagate in networks, a process relevant to cognitive mechanisms, remains less explored. In this work, we propose a model to investigate the propagation of an external signal in a network with heterogeneously distributed natural frequencies. We begin with a star network in which the hub node has a higher natural frequency than the leaf nodes. An external signal is applied to one leaf node (the source node). Interestingly, we observe a phenomenon of remote propagation (RP), where the external signal becomes phase-locked not to the source or hub node but to an indirectly connected leaf node. We further demonstrate that RP persists in more complex network topologies. Additionally, RP can be enhanced by using multiple source nodes and can even lead to double phase-locking, i.e., a finding that may offer insights into signal transmission in brain networks. Finally, we provide a theoretical analysis to explain the RP mechanism and evaluate signal transmission efficacy.