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

doi:10.1016/j.jde.2014.05.054

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

37 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 language	English
Pages (from-to)	2591-2621
Number of pages	31
Journal	Journal of Differential Equations
Volume	257
Issue number	7
DOIs	https://doi.org/10.1016/j.jde.2014.05.054
Publication status	Published - 2014 Oct 1

Bibliographical note

Funding Information:
Y.-P. Choi was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2012R1A6A3A03039496 ). Z. Li was supported by 973 Program ( 2012CB215201 ) and KRF-2009-0093137 ( Korea Research Foundation ). S.-Y. Ha was partially supported by KRF-2011-0015388 ( Korea Research Foundation ). X. Xue was supported by NSF of China grant 11271099 .

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/j.jde.2014.05.054

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title = "Complete entrainment of Kuramoto oscillators with inertia on networks via gradient-like flow",

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.",

author = "Choi, {Young Pil} and Zhuchun Li and Ha, {Seung Yeal} and Xiaoping Xue and Yun, {Seok Bae}",

note = "Funding Information: Y.-P. Choi was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2012R1A6A3A03039496 ). Z. Li was supported by 973 Program ( 2012CB215201 ) and KRF-2009-0093137 ( Korea Research Foundation ). S.-Y. Ha was partially supported by KRF-2011-0015388 ( Korea Research Foundation ). X. Xue was supported by NSF of China grant 11271099 . ",

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AU - Xue, Xiaoping

AU - Yun, Seok Bae

N1 - Funding Information: Y.-P. Choi was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2012R1A6A3A03039496 ). Z. Li was supported by 973 Program ( 2012CB215201 ) and KRF-2009-0093137 ( Korea Research Foundation ). S.-Y. Ha was partially supported by KRF-2011-0015388 ( Korea Research Foundation ). X. Xue was supported by NSF of China grant 11271099 .

PY - 2014/10/1

Y1 - 2014/10/1

N2 - 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.

AB - 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.

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

Abstract

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