Dynamic link switching induces stable synchronized states in sparse networks

Abstract: The flow of information in networked systems composed of multiple interacting elements strongly depends on the level of connectivity among these elements. Sparse connectivity often hinders the emergence of states where information is globally shared, such as fully synchronized states. In this context, dynamically switching the existing network links among the system elements can facilitate the onset of synchronization. However, determining the optimal rate at which links should be switched to ensure asymptotically stable synchronized behavior remains an open question. Here, we address this issue in a double-layer network of FitzHugh-Nagumo oscillators with sparse inter-layer connectivity. Specifically, we demonstrate that faster switching of the inter-layer links, which sweeps through a more significant number of oscillators, is more effective in establishing inter-layer synchronization than maintaining links on the identical oscillators for extended durations. We also evaluate the effectiveness of fast-switching links as the layer size increases. In a reduced system, we introduce smooth square-wave functions to emulate link switching, eventually introducing discontinuities into the system dynamics. This approach enables the assessment of the transverse stability of synchronized states induced by switching links.