Collective behavior

Finance

Self-organization

Synchronization networks

Combinatorics

Physics

Statistical physics

Hysteresis

Coupling (piping)

World Wide Web

Sociology

Artificial intelligence

Nonlinear system

Economics

Order (exchange)

Topology (electrical circuits)

Pairwise comparison

Anthropology

Metallurgy

Materials science

Living systems

Synchronization (alternating current)

Mathematics

Complex network

Computer science

Phase (matter)

Complex system

Quantum mechanics

Bistability

Communications Physics

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.

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