The complementary contribution of each order topology into the synchronization of multi-order networks

Higher-order interactions improve our capability to model real-world complex systems ranging from physics and neuroscience to economics and social sciences. There is great interest nowadays in understanding the contribution of higher-order terms to the collective behavior of the network. In this work, we investigate the stability of complete synchronization of complex networks with higher-order structures. We demonstrate that the synchronization level of a network composed of nodes interacting simultaneously via multiple orders is maintained regardless of the intensity of coupling strength across different orders. We articulate that lower-order and higher-order topologies work together complementarily to provide the optimal stable configuration, challenging previous conclusions that higher-order interactions promote the stability of synchronization. Furthermore, we find that simply adding higher-order interactions based on existing connections, as in simple complexes, does not have a significant impact on synchronization. The universal applicability of our work lies in the comprehensive analysis of different network topologies, including hypergraphs and simplicial complexes, and the utilization of appropriate rescaling to assess the impact of higher-order interactions on synchronization stability.

Automated summary

Higher-order interactions play a crucial role in modeling complex systems. In our study, we investigated the stability of synchronization in complex networks with higher-order structures. Surprisingly, we found that the synchronization level remains unaffected by the intensity of coupling strength across different orders. Our results challenge the previous notion that higher-order interactions promote synchronization stability and instead demonstrate that lower-order and higher-order topologies work together to provide the optimal stable configuration. Additionally, we discovered that simply adding higher-order interactions based on existing connections does not significantly impact synchronization. Our work, which includes a comprehensive analysis of different network topologies and appropriate rescaling, has universal applicability in assessing the impact of higher-order interactions on synchronization stability.