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arXiv · 2506.06791

How do higher-order interactions shape the energy landscape?

Zheng Wang·Wenchang Qi·Jinjie Zhu·Xianbin Liu
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Abstract

Understanding how higher-order interactions shape the energy landscape of coupled oscillator networks is crucial for characterizing complex synchronization phenomena. Here, we investigate a generalized Kuramoto model with triadic interactions, combining deterministic basin analysis, noise-induced transitions, and quantum annealing methods. We uncover a dual effect of higher-order interactions: they simultaneously expand basins for non-twisted states while contracting those of twisted states, yet modify potential well depths for both. As triadic coupling strengthens, higher-winding-number states and non-twisted states gain stability relative to synchronized states. The system exhibits remarkable stability asymmetry, where states with small basins can possess deep potential wells, making them highly resistant to noise-induced transitions once formed. These findings extend quasipotential theory to high-dimensional networked systems and offer new insights for controlling synchronization in complex systems.

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Zheng Wang, Wenchang Qi, Jinjie Zhu, Xianbin Liu. 2025-06-07. How do higher-order interactions shape the energy landscape?. https://doi.org/10.1103/zqf8-tg6g

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