How do higher-order interactions shape the energy landscape?

TL;DR

This paper explores how triadic higher-order interactions influence the energy landscape of coupled oscillators, revealing their dual role in stabilizing certain states and extending quasipotential theory to complex networks.

Contribution

It introduces a generalized Kuramoto model with triadic interactions and applies diverse analysis methods to uncover how higher-order interactions shape stability and synchronization.

Findings

Higher-order interactions expand basins for non-twisted states.

They contract basins for twisted states but deepen potential wells.

States with small basins can be highly resistant to noise.

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.