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- Title
Remarks on the complete synchronization for the Kuramoto model with frustrations.
- Authors
Ha, Seung-Yeal; Kim, Hwa Kil; Park, Jinyeong
- Abstract
The synchronous dynamics of many limit-cycle oscillators can be described by phase models. The Kuramoto model serves as a prototype model for phase synchronization and has been extensively studied in the last 40 years. In this paper, we deal with the complete synchronization problem of the Kuramoto model with frustrations on a complete graph. We study the robustness of complete synchronization with respect to the network structure and the interaction frustrations, and provide sufficient frameworks leading to the complete synchronization, in which all frequency differences of oscillators tend to zero asymptotically. For a uniform frustration and unit capacity, we extend the applicable range of initial configurations for the complete synchronization to be distributed on larger arcs than a half circle by analyzing the detailed dynamics of the order parameters. This improves the earlier results [S.-Y. Ha, H. Kim and J. Park, Remarks on the complete frequency synchronization of Kuramoto oscillators, Nonlinearity 28 (2015) 1441-1462; Z. Li and S.-Y. Ha, Uniqueness and well-ordering of emergent phase-locked states for the Kuramoto model with frustration and inertia, Math. Models Methods Appl. Sci. 26 (2016) 357-382.] which can be applicable only for initial configurations confined in a half circle.
- Subjects
LIMIT cycles; PARAMETRONS; COMPLETE graphs; MATHEMATICAL models; ROBUST statistics; SYNCHRONIZATION
- Publication
Analysis & Applications, 2018, Vol 16, Issue 4, p525
- ISSN
0219-5305
- Publication type
Article
- DOI
10.1142/S0219530517500130