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Three-body interactions unveil devil's staircase, multistability, and synchronization revival in phase oscillators
Hancheng Li1, Xuan Wang1, Jinfeng Liang1
1Beijing University of Posts and Telecommunications, School of Physical Science and Technology, Beijing 100876, People's Republic of China.
Physical Review. E
|February 20, 2026
Summary
This study explores three-body interactions in coupled oscillators, revealing complex synchronization patterns like devil
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Statistical Physics
Background:
- Collective behavior often relies on pairwise interactions.
- Higher-order interactions are crucial for complex dynamics but less understood.
- Minimal models are needed to isolate and study these effects.
Purpose of the Study:
- Investigate synchronization in a minimal model with pure three-body interactions.
- Analyze dynamics beyond traditional pairwise coupling.
- Understand the role of higher-order interactions in collective behavior.
Main Methods:
- Developed a minimal model of three nonidentical phase oscillators.
- Focused exclusively on pure three-body interactions.
- Analyzed rotation numbers, Arnold tongues, and attractor basin stability.
Main Results:
- Observed a complete devil's staircase in rotation numbers, structured by an anomalous Farey sequence.
- Found robust multistability with coexisting synchronous and other regimes.
- Arnold tongues showed nonmonotonic behavior, preventing chaos.
- Synchronous states reappeared at weak coupling strengths.
Conclusions:
- Pure three-body interactions lead to complex synchronization phenomena.
- System dynamics are rich and deviate from pairwise coupling predictions.
- Provides insights for controlling synchronization in various systems.
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