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Emergence of higher-order interactions in systems of coup...
[Submitted on 18 Dec 2025 (v1), last revised 23 Jun 2026 (this v · 2026-06-24 · via math updates on arXiv.org

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Abstract:We show that higher-order interactions naturally emerge from time-delayed pairwise coupling in Kuramoto oscillators. By expanding the delayed pairwise coupling to the second order, we derive a delay-free Kuramoto model possessing both pairwise and three-body interactions. Numerical simulations and stability analysis demonstrate that the three-body Kuramoto model and the time-delayed pairwise Kuramoto model exhibit qualitatively consistent synchronization transitions under appropriate conditions. In particular, the bistability arising in the time-delayed Kuramoto model is accounted for by the three-body interactions. Our findings reveal that time delays can be recast effectively as higher-order interactions, providing an insight into how coupling delays shape collective dynamics.

Submission history

From: Riccardo Muolo [view email]
[v1] Thu, 18 Dec 2025 05:33:16 UTC (1,044 KB)
[v2] Tue, 23 Jun 2026 06:38:26 UTC (1,646 KB)