Leader–follower coherence in multi-layer networks: Understanding allocations of leaders

Yixin Wang, Jun Wang and Weigang Sun
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Yixin Wang: Department of Mathematics, School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, P. R. China
Jun Wang: Department of Mathematics, School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, P. R. China
Weigang Sun: Department of Mathematics, School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, P. R. China

International Journal of Modern Physics C (IJMPC), 2024, vol. 35, issue 07, 1-12

Abstract: This paper investigates a leader–follower consensus problem of multi-layer networks and understands the role of leader’s allocations in the process of consensus. Leader–follower coherence quantified by the spectrum measures the extent of consensus between leaders and followers in the system under additive noise. In order to study the exact interplay between leader–follower coherence and leader’s allocations, we choose complete multi-partite networks as network models and assign the leaders into different layers. Based on the network construction, we obtain exact solutions of leader–follower coherence with freely assigned leaders and reveal that the allocations of leaders have a significant impact on the coherence. Finally, we compare the leader–follower coherence and leaderless coherence of bipartite networks when the number of leaders and network size satisfies certain conditions.

Keywords: Consensus; leader–follower coherence; multi-layer network (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S012918312450092X

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