Higher-order interactions in complex networks of phase oscillators promote abrupt synchronization switching
Synchronization dynamics of network-coupled oscillators represents an important area of research in nonlinear science and complex networks. Applications where synchronization plays a critical role in a system's functionality include cardiac rhythms, power grid dynamics, and proper cell circuit behavior. The interplay between structure and dynamics in such systems gives rise to novel nonlinear phenomena like switch-like abrupt transitions to synchronization and cluster states. Recent work in physics and neuroscience have specifically highlighted the importance of higher-order interactions between dynamical units, i.e., three- and four-way interactions in addition to pair-wise 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 systems, without the need of particular correlation mechanisms between the oscillators and the topological structure.