Quantized Frequency-locking and Extreme Transitions in a Ring of Phase Oscillators with Three-Body Interactions

TL;DR

This paper explores exotic frequency-locked states in a ring of phase oscillators with three-body interactions, revealing a rich landscape of synchronization phenomena and phase transitions driven by heterogeneity.

Contribution

It introduces a minimal model demonstrating how higher-order interactions create complex synchronization states and extreme transitions in oscillator populations.

Findings

Existence of stable quantized frequency-locked states without phase coherence

Heterogeneity broadens frequency levels into continuous bands

Identification of a second-order transition from locking to desynchronization

Abstract

We report a spectrum of exotic frequency-locked states in a ring of phase oscillators with pure three-body interactions. For identical oscillators, the system hosts a vast multiplicity of stable quantized frequency-locked states without phase coherence. Introducing frequency heterogeneity broadens each quantized level into a continuous band and drives an extreme second-order transition at $\Delta_c$: below $\Delta_c$ the entire population locks to a collective phase velocity; above $\Delta_c$ a desynchronous state emerges, characterized by strongly localized bursts on a slowly varying background. This minimal model thus establishes a new paradigm for complex synchronization landscapes arising from higher-order interactions.