  Synchronization processes play critical roles in the functionality of a wide
range of both natural and man-made systems. Recent work in physics and
neuroscience highlights the importance of higher-order interactions between
dynamical units, i.e., three- and four-way interactions in addition to pairwise
interactions, and their role in shaping collective behavior. Here we show that
higher-order interactions between coupled phase oscillators, encoded
microscopically in a simplicial complex, give rise to added nonlinearity in the
macroscopic system dynamics that induces abrupt synchronization transitions via
hysteresis and bistability of synchronized and incoherent states. Moreover,
these higher-order interactions can stabilize strongly synchronized states even
when the pairwise coupling is repulsive. These findings reveal a self-organized
phenomenon that may be responsible for the rapid switching to synchronization
in many biological and other systems that exhibit synchronization without the
need of particular correlation mechanisms between the oscillators and the
topological structure.
