Hypernetworks induce stable hyperlocking.

Hypernetworks capture coupling structures where interactions extend beyond pairs to groups of three or more units, called hyperedges. They are of increasing importance for many systems such as the brain, social groups, ecosystems, and the climate. We describe here a synchronization phenomenon that is distinctive for hypernetworks. We uncover that in a system of three coupled oscillators with resonant frequencies, the coupling by a triadic hypernetwork motif, where a third node modulates the interaction between two others, can induce a stable locking of a phase triplet, while no pairwise locking is observed. Using normal form transformations and phase reduction, we derive analytically how a specific choice of the coupling functions induces this hyperlocking. We confirm our predictions with both numerical simulations and chemical experiments. Our findings uncover a new synchronization mechanism intrinsic to higher-order interactions and open new directions for controlling real-world complex dynamics beyond pairwise frameworks.