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

Author:

Yuanzhao Zhang, Per Sebastian Skardal, Federico Battiston, Giovanni Petri, Maxime Lucas

Keyword:

Nonlinear Sciences, Adaptation and Self-Organizing Systems, Adaptation and Self-Organizing Systems (nlin.AO), Dynamical Systems (math.DS), Pattern Formation and Solitons (nlin.PS)

journal:

date:

2023-09-27 16:00:00

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.

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