Higher-order interactions in complex networks of phase oscillators promote abrupt synchronization switching

TL;DR

This paper demonstrates that higher-order interactions in complex oscillator networks cause abrupt synchronization transitions and bistability, explaining rapid switching phenomena in biological and artificial systems.

Contribution

It reveals that higher-order interactions encoded in simplicial complexes induce nonlinear dynamics leading to hysteresis and bistability in synchronization.

Findings

Higher-order interactions cause abrupt synchronization transitions.

These interactions induce hysteresis and bistability.

They can stabilize synchronization even with repulsive pairwise coupling.

Abstract

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.