Complete entrainment of Kuramoto oscillators with inertia on networks via gradient-like flow

Young Pil Choi, Zhuchun Li, Seung Yeal Ha, Xiaoping Xue, Seok Bae Yun

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

We study the asymptotic complete entrainment of Kuramoto oscillators with inertia on symmetric and connected network. We provide several sufficient conditions for the asymptotic complete entrainment in terms of initial phase-frequency configurations, strengths of inertia and coupling, and natural frequency distributions. For this purpose, we reinterpret the Kuramoto oscillators with inertia as a second-order gradient-like flow, and adopt analytical methods based on several Lyapunov functions to apply the convergence estimate studied by Haraux and Jendoubi [21]. Our approach does not require any spectral information of the graph associated with the given network structure.

Original languageEnglish
Pages (from-to)2591-2621
Number of pages31
JournalJournal of Differential Equations
Volume257
Issue number7
DOIs
Publication statusPublished - 2014 Oct 1

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Entrainment
Lyapunov functions
Inertia
Natural frequencies
Gradient
Convergence Estimates
Natural Frequency
Analytical Methods
Network Structure
Lyapunov Function
Configuration
Sufficient Conditions
Graph in graph theory

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

Choi, Young Pil ; Li, Zhuchun ; Ha, Seung Yeal ; Xue, Xiaoping ; Yun, Seok Bae. / Complete entrainment of Kuramoto oscillators with inertia on networks via gradient-like flow. In: Journal of Differential Equations. 2014 ; Vol. 257, No. 7. pp. 2591-2621.
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Complete entrainment of Kuramoto oscillators with inertia on networks via gradient-like flow. / Choi, Young Pil; Li, Zhuchun; Ha, Seung Yeal; Xue, Xiaoping; Yun, Seok Bae.

In: Journal of Differential Equations, Vol. 257, No. 7, 01.10.2014, p. 2591-2621.

Research output: Contribution to journalArticle

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