CONSENSUS DYNAMICS WITH LEADER SELECTION IN HEXAGONAL NETWORKS

Zhiqiang Wu (), Yumei Xue (), Huixia He (), Cheng Zeng and Wenjie Wang ()
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Zhiqiang Wu: School of Mathematical Sciences, Beihang University, Beijing 100083, P. R. China
Yumei Xue: School of Mathematical Sciences, Beihang University, Beijing 100083, P. R. China
Huixia He: School of Mathematical Sciences, Beihang University, Beijing 100083, P. R. China
Cheng Zeng: ��School of Mathematics and Information Science, Shandong Technology and Business University, Yantai 264003, P. R. China
Wenjie Wang: School of Mathematical Sciences, Beihang University, Beijing 100083, P. R. China

FRACTALS (fractals), 2025, vol. 33, issue 07, 1-19

Abstract: This study investigates the noise consensus dynamics in a class of networks with an initial hexagonal structure, where the vertices are subjected to white noise. Leveraging the network’s self-similarity, a comprehensive spectral analysis is conducted. The research further explores the first- and second-order coherence in networks without leader nodes, as well as the first- and second-order coherence in networks with a single leader node and the first-order coherence in networks with dual leader nodes. Based on the specific topological properties of the network, explicit formulas for coherence under each consensus algorithm are derived. Taking UAV swarms as a representative example, the implications of the findings for leader node selection in multi-agent systems are analyzed, providing valuable theoretical insights into optimizing network performance.

Keywords: Consensus; Coherence; Multi-Agent System; Leaderless Coherence; Leader–Follower Coherence (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X2550063X

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