Complete synchronization of Kuramoto oscillators with finite inertia

Young Pil Choi; Seung Yeal Ha; Seok Bae Yun

doi:10.1016/j.physd.2010.08.004

Complete synchronization of Kuramoto oscillators with finite inertia

Young Pil Choi
, Seung Yeal Ha
, Seok Bae Yun

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

115 Scopus citations

Abstract

We present an approach based on Gronwall's inequalities for the asymptotic complete phasefrequency synchronization of Kuramoto oscillators with finite inertia. For given finite inertia and coupling strength, we present admissible classes of initial configurations and natural frequency distributions, which lead to the complete phasefrequency synchronization asymptotically. For this, we explicitly identify invariant regions for the Kuramoto flow, and derive second-order Gronwall's inequalities for the evolution of phase and frequency diameters. Our detailed time-decay estimates for phase and frequency diameters are independent of the number of oscillators. We also compare our analytical results with numerical simulations.

Original language	English
Pages (from-to)	32-44
Number of pages	13
Journal	Physica D: Nonlinear Phenomena
Volume	240
Issue number	1
DOIs	https://doi.org/10.1016/j.physd.2010.08.004
State	Published - 1 Jan 2011
Externally published	Yes

Keywords

Complete synchronization
Frequency
Inertia effects
Kuramoto model
Phase

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10.1016/j.physd.2010.08.004

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title = "Complete synchronization of Kuramoto oscillators with finite inertia",

abstract = "We present an approach based on Gronwall's inequalities for the asymptotic complete phasefrequency synchronization of Kuramoto oscillators with finite inertia. For given finite inertia and coupling strength, we present admissible classes of initial configurations and natural frequency distributions, which lead to the complete phasefrequency synchronization asymptotically. For this, we explicitly identify invariant regions for the Kuramoto flow, and derive second-order Gronwall's inequalities for the evolution of phase and frequency diameters. Our detailed time-decay estimates for phase and frequency diameters are independent of the number of oscillators. We also compare our analytical results with numerical simulations.",

keywords = "Complete synchronization, Frequency, Inertia effects, Kuramoto model, Phase",

author = "Choi, \{Young Pil\} and Ha, \{Seung Yeal\} and Yun, \{Seok Bae\}",

year = "2011",

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doi = "10.1016/j.physd.2010.08.004",

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journal = "Physica D: Nonlinear Phenomena",

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T1 - Complete synchronization of Kuramoto oscillators with finite inertia

AU - Choi, Young Pil

AU - Ha, Seung Yeal

AU - Yun, Seok Bae

PY - 2011/1/1

Y1 - 2011/1/1

N2 - We present an approach based on Gronwall's inequalities for the asymptotic complete phasefrequency synchronization of Kuramoto oscillators with finite inertia. For given finite inertia and coupling strength, we present admissible classes of initial configurations and natural frequency distributions, which lead to the complete phasefrequency synchronization asymptotically. For this, we explicitly identify invariant regions for the Kuramoto flow, and derive second-order Gronwall's inequalities for the evolution of phase and frequency diameters. Our detailed time-decay estimates for phase and frequency diameters are independent of the number of oscillators. We also compare our analytical results with numerical simulations.

AB - We present an approach based on Gronwall's inequalities for the asymptotic complete phasefrequency synchronization of Kuramoto oscillators with finite inertia. For given finite inertia and coupling strength, we present admissible classes of initial configurations and natural frequency distributions, which lead to the complete phasefrequency synchronization asymptotically. For this, we explicitly identify invariant regions for the Kuramoto flow, and derive second-order Gronwall's inequalities for the evolution of phase and frequency diameters. Our detailed time-decay estimates for phase and frequency diameters are independent of the number of oscillators. We also compare our analytical results with numerical simulations.

KW - Complete synchronization

KW - Frequency

KW - Inertia effects

KW - Kuramoto model

KW - Phase

UR - https://www.scopus.com/pages/publications/78649328720

U2 - 10.1016/j.physd.2010.08.004

DO - 10.1016/j.physd.2010.08.004

M3 - Article

AN - SCOPUS:78649328720

SN - 0167-2789

VL - 240

SP - 32

EP - 44

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 1

ER -

Complete synchronization of Kuramoto oscillators with finite inertia

Abstract

Keywords

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