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arXiv · 2512.18983

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

Jinfeng Liang·Shanshan Zhu·Yang Li·Qionglin Dai·Haihong Li·Junzhong Yang
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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 $Δ_c$: below $Δ_c$ the entire population locks to a collective phase velocity; above $Δ_c$ 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.

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Jinfeng Liang, Shanshan Zhu, Yang Li, Qionglin Dai, Haihong Li, Junzhong Yang. 2025-12-22. Quantized Frequency-locking and Extreme Transitions in a Ring of Phase Oscillators with Three-Body Interactions. https://arxiv.org/abs/2512.18983

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