Communications in Mathematical Sciences

Volume 12 (2014)

Number 3

Complete synchronization of Kuramoto oscillators with hierarchical leadership

Pages: 485 – 508

DOI: http://dx.doi.org/10.4310/CMS.2014.v12.n3.a5

Authors

Seung-Yeal Ha (Department of Mathematical Sciences, Seoul National University, Seoul, South Korea)

Zhuchun Li (Department of Mathematics, Harbin Institute of Technology, Harbin, China)

Abstract

We study the asymptotic emergence of the complete synchronization of Kuramoto oscillators with hierarchical leadership. We show that asymptotic complete frequency synchronization occurs for some class of initial phase configurations, when Kuramoto oscillators are scattered on the nodes of a directed graph with a hierarchical leadership topology and the coupling strength is sufficiently large. This generalizes previous studies on the complete synchronization of Kuramoto oscillators on connected and symmetric graphs. We also provide several numerical results to confirm our analytical results.

Keywords

Kuramoto oscillators, hierarchical leadership, complete synchronization

2010 Mathematics Subject Classification

34C15, 92D25

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