中国物理B ›› 2025, Vol. 34 ›› Issue (7): 70502-070502.doi: 10.1088/1674-1056/adcded

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Optimal synchronization of higher-order Kuramoto model on hypergraphs

Chong-Yang Wang(王重阳)1,2,3,†, Bi-Yun Ji(季碧芸)1,2, and Linyuan Lü(吕琳媛)4,‡1   

  1. 1 Yangtze Delta Region Institute of University of Electronic Science and Technology of China, Huzhou 313000, China;
    2 Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China;
    3 Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, and Key Laboratory of Quantum Theory and Applications of Ministry of Education, Lanzhou University, Lanzhou 730000, China;
    4 School of Cyber Science and Technology, University of Science and Technology of China, Hefei 230026, China
  • 收稿日期:2025-02-10 修回日期:2025-04-08 接受日期:2025-04-17 出版日期:2025-06-18 发布日期:2025-07-07
  • 通讯作者: Chong-Yang Wang, Linyuan Lü E-mail:wangchongyang@csj.uestc.edu.cn;linyuan.lv@uestc.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 12247153, T2293771, and 12247101), the Zhejiang Provincial Natural Science Foundation of China (Grant No. LTGY24A050002), the Sichuan Science and Technology Program (Grant Nos. 2024NSFSC1364 and 2023NSFSC1919), the Project of Huzhou Science and Technology Bureau (Grant No. 2022YZ29), the UESTCYDRI research start-up (Grant No. U03210066), and the New Cornerstone Science Foundation through the Xplorer Prize.

Optimal synchronization of higher-order Kuramoto model on hypergraphs

Chong-Yang Wang(王重阳)1,2,3,†, Bi-Yun Ji(季碧芸)1,2, and Linyuan Lü(吕琳媛)4,‡1   

  1. 1 Yangtze Delta Region Institute of University of Electronic Science and Technology of China, Huzhou 313000, China;
    2 Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China;
    3 Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, and Key Laboratory of Quantum Theory and Applications of Ministry of Education, Lanzhou University, Lanzhou 730000, China;
    4 School of Cyber Science and Technology, University of Science and Technology of China, Hefei 230026, China
  • Received:2025-02-10 Revised:2025-04-08 Accepted:2025-04-17 Online:2025-06-18 Published:2025-07-07
  • Contact: Chong-Yang Wang, Linyuan Lü E-mail:wangchongyang@csj.uestc.edu.cn;linyuan.lv@uestc.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 12247153, T2293771, and 12247101), the Zhejiang Provincial Natural Science Foundation of China (Grant No. LTGY24A050002), the Sichuan Science and Technology Program (Grant Nos. 2024NSFSC1364 and 2023NSFSC1919), the Project of Huzhou Science and Technology Bureau (Grant No. 2022YZ29), the UESTCYDRI research start-up (Grant No. U03210066), and the New Cornerstone Science Foundation through the Xplorer Prize.

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摘要： Complex networks play a crucial role in the study of collective behavior, encompassing the analysis of dynamical properties and network topology. In real-world systems, higher-order interactions among multiple entities are widespread and significantly influence collective dynamics. Here, we extend the synchronization alignment function framework to hypergraphs of arbitrary order by leveraging the multi-order Laplacian matrix to encode higher-order interactions. Our findings reveal that the upper bound of synchronous behavior is determined by the maximum eigenvalue of the multi-order Laplacian matrix. Furthermore, we decompose the contribution of each hyperedge to this eigenvalue and utilize it as a basis for designing an eigenvalue-based topology modification algorithm. This algorithm effectively enhances the upper bound of synchronous behavior without altering the total number of higher-order interactions. Our study provides new insights into dynamical optimization and topology tuning in hypergraphs, advancing the understanding of the interplay between higher-order interactions and collective dynamics.

关键词: synchronization optimization, hypergraph, complex network

Abstract: Complex networks play a crucial role in the study of collective behavior, encompassing the analysis of dynamical properties and network topology. In real-world systems, higher-order interactions among multiple entities are widespread and significantly influence collective dynamics. Here, we extend the synchronization alignment function framework to hypergraphs of arbitrary order by leveraging the multi-order Laplacian matrix to encode higher-order interactions. Our findings reveal that the upper bound of synchronous behavior is determined by the maximum eigenvalue of the multi-order Laplacian matrix. Furthermore, we decompose the contribution of each hyperedge to this eigenvalue and utilize it as a basis for designing an eigenvalue-based topology modification algorithm. This algorithm effectively enhances the upper bound of synchronous behavior without altering the total number of higher-order interactions. Our study provides new insights into dynamical optimization and topology tuning in hypergraphs, advancing the understanding of the interplay between higher-order interactions and collective dynamics.

Key words: synchronization optimization, hypergraph, complex network

中图分类号:  (Synchronization; coupled oscillators)

  • 05.45.Xt
05.10.-a (Computational methods in statistical physics and nonlinear dynamics) 64.60.aq (Networks)