Deeper but smaller: Higher-order interactions increase linear stability but shrink basins

TL;DR

This paper investigates how higher-order interactions in hypergraph-structured Kuramoto oscillators affect collective dynamics, revealing they can stabilize certain states linearly but reduce their basin sizes, impacting global stability.

Contribution

It demonstrates that higher-order interactions can simultaneously increase linear stability and decrease basin stability, providing new insights into the global effects of complex interactions.

Findings

Higher-order interactions stabilize twisted states linearly.

They reduce the basin size of stable states.

This dual effect impacts the predictability of collective dynamics.

Abstract

A key challenge of nonlinear dynamics and network science is to understand how higher-order interactions influence collective dynamics. Although many studies have approached this question through linear stability analysis, less is known about how higher-order interactions shape the global organization of different states. Here, we shed light on this issue by analyzing the rich patterns supported by identical Kuramoto oscillators on hypergraphs. We show that higher-order interactions can have opposite effects on linear stability and basin stability: they stabilize twisted states (including full synchrony) by improving their linear stability, but also make them hard to find by dramatically reducing their basin size. Our results highlight the importance of understanding higher-order interactions from both local and global perspectives.