How do higher-order interactions shape the energy landscape?
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.
Keywords
Cite
@article{arxiv.2506.06791,
title = {How do higher-order interactions shape the energy landscape?},
author = {Zheng Wang and Wenchang Qi and Jinjie Zhu and Xianbin Liu},
journal= {arXiv preprint arXiv:2506.06791},
year = {2026}
}