  The emergence of collective behaviors in networks of dynamical units in
pairwise interaction has been explained as the effect of diffusive coupling.
How does the presence of higher-order interaction impact the onset of
spontaneous or induced synchronous behavior? Inspired by actuation and
measurement constraints typical of physical and engineered systems, we propose
a diffusion mechanism over hypergraphs that explains the onset of
synchronization through a clarifying analogy with signed graphs. Our findings
are mathematically backed by general conditions for convergence to the
synchronous state.
