Source-linked AI summary
Higher-order interactions in complex networks of phase oscillators promote abrupt synchronization switching
Per Sebastian Skardal, Alex Arenas
TL;DR
The paper asks how abrupt synchronization switching can arise in heterogeneous phase oscillators without special network–dynamics correlations. It studies 1-, 2-, and 3-simplex interactions on simplicial complexes and finds that higher-order interactions induce abrupt, hysteretic synchronization transitions and can stabilize synchronization under repulsive pairwise coupling.
Problem
The mechanisms producing bistability and fast switching between incoherent and synchronized states remain unclear, while network wiring varies across individuals.
Method
The authors analyze heterogeneous phase oscillators with 1-, 2-, and 3-simplex interactions encoded by simplicial-complex adjacency structures, including a three-layer multiplex construction.
Results
Higher-order interactions generate macroscopic nonlinearities that produce abrupt synchronization transitions with hysteresis and bistability, and stabilize synchronized states when pairwise coupling is repulsive.
Takeaways & Limitations
These interactions provide a self-organized mechanism for rapid switching between resting-like incoherent and active-like synchronized states without additional dynamical or structural ingredients.
Abstract
from arXiv · showhide
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.