Emergence of synchronization in Kuramoto model with general digraph

DOI10.3934/DCDSB.2022172zbMATH Open1511.34062arXiv2107.06487MaRDI QIDQ6372749

Publication date: 14 July 2021

Abstract: In this paper, we study the complete synchronization of the Kuramoto model with general network containing a spanning tree, when the initial phases are distributed in an open half circle. As lack of uniform coercivity in general digraph, in order to capture the dissipation structure on a general network, we apply the node decomposition criteria in cite{H-L-Z20} to yield a hierarchical structure, which leads to the hypo-coercivity. This drives the phase diameter into a small region after finite time in a large coupling regime, and the uniform boundedness of the diameter eventually leads to the emergence of exponentially fast synchronization.

Mathematics Subject Classification ID

Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Directed graphs (digraphs), tournaments (05C20) Synchronization of solutions to ordinary differential equations (34D06)

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