Communications in Mathematical Sciences
Volume 12 (2014)
Complete synchronization of Kuramoto oscillators with hierarchical leadership
Pages: 485 – 508
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.
Kuramoto oscillators, hierarchical leadership, complete synchronization
2010 Mathematics Subject Classification