Higher-order interactions induce anomalous transitions to synchrony

TL;DR

This paper demonstrates that higher-order interactions in coupled oscillators cause unusual synchronization transitions, including multistability and slow switching, differing from traditional models like Kuramoto.

Contribution

It introduces a model with two- and three-body interactions, revealing novel synchronization phenomena and phase transition scenarios not seen in classical models.

Findings

Higher-order interactions induce multistability of synchronization states.

Transitions to synchrony occur via slow switching and clustering.

Similar phenomena persist with small heterogeneity in oscillator frequencies.

Abstract

We analyze the simplest model of identical coupled phase oscillators subject to two-body and three-body interactions with permutation symmetry. This model is derived from an ensemble of weakly coupled nonlinear oscillators by phase reduction. Our study indicates that higher-order interactions induce anomalous transitions to synchrony. Unlike the conventional Kuramoto model, higher-order interactions lead to anomalous phenomena such as multistability of full synchronization, incoherent, and two-cluster states, and transitions to synchrony through slow switching and clustering. Phase diagrams of the dynamical regimes are constructed theoretically and verified by direct numerical simulations. We also show that similar transition scenarios are observed even if a small heterogeneity in the oscillators' frequency is included.