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Hauptverfasser:	Zhang, Yuanzhao, Skardal, Per Sebastian, Battiston, Federico, Petri, Giovanni, Lucas, Maxime
Format:	Preprint
Veröffentlicht:	2023
Schlagworte:	Adaptation and Self-Organizing Systems Dynamical Systems Pattern Formation and Solitons
Online-Zugang:	https://arxiv.org/abs/2309.16581
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author	Zhang, Yuanzhao Skardal, Per Sebastian Battiston, Federico Petri, Giovanni Lucas, Maxime
author_facet	Zhang, Yuanzhao Skardal, Per Sebastian Battiston, Federico Petri, Giovanni Lucas, Maxime
contents	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.
format	Preprint
id	arxiv_https___arxiv_org_abs_2309_16581
institution	arXiv
publishDate	2023
record_format	arxiv
spellingShingle	Deeper but smaller: Higher-order interactions increase linear stability but shrink basins Zhang, Yuanzhao Skardal, Per Sebastian Battiston, Federico Petri, Giovanni Lucas, Maxime Adaptation and Self-Organizing Systems Dynamical Systems Pattern Formation and Solitons 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.
title	Deeper but smaller: Higher-order interactions increase linear stability but shrink basins
topic	Adaptation and Self-Organizing Systems Dynamical Systems Pattern Formation and Solitons
url	https://arxiv.org/abs/2309.16581

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