Understanding how higher-order interactions affect collective behavior is a central problem in nonlinear dynamics and complex systems. Most works have focused on a single higher-order coupling function, neglecting other viable choices. Here we study coupled oscillators with dyadic and three different types of higher-order couplings. By analyzing the stability of different twisted states on rings, we show that many states are stable only for certain combinations of higher-order couplings, and thus the full range of system dynamics cannot be observed unless all types of higher-order couplings are simultaneously considered.
@article{arxiv.2510.09387,
title = {Mixed higher-order coupling stabilizes new states},
author = {Per Sebastian Skardal and Federico Battiston and Maxime Lucas and Matthew S Mizuhara and Giovanni Petri and Yuanzhao Zhang},
journal= {arXiv preprint arXiv:2510.09387},
year = {2025}
}