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Deeper but smaller: Higher-order interactions increase linear stability but shrink basins. (arXiv:2309.16581v1 [nlin.AO])

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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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