Low-dimensional behavior of Kuramoto model with inertia in complex networks

Peng Ji; Thomas K. D. M. Peron; Francisco A. Rodrigues; Juergen Kurths

doi:10.1038/srep04783

Low-dimensional behavior of Kuramoto model with inertia in complex networks

Peng Ji^*, Thomas K. D. M. Peron, Francisco A. Rodrigues, Juergen Kurths

^*Corresponding author for this work

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Abstract

Low-dimensional behavior of large systems of globally coupled oscillators has been intensively investigated since the introduction of the Ott-Antonsen ansatz. In this report, we generalize the Ott-Antonsen ansatz to second-order Kuramoto models in complex networks. With an additional inertia term, we find a low-dimensional behavior similar to the first-order Kuramoto model, derive a self-consistent equation and seek the time-dependent derivation of the order parameter. Numerical simulations are also conducted to verify our analytical results.

Original language	English
Article number	4783
Number of pages	6
Journal	Scientific Reports
Volume	4
DOIs	https://doi.org/10.1038/srep04783
Publication status	Published - 2 May 2014

Bibliographical note

Z. K. Gao was supported by National Natural Science Foundation of China under Grant No. 61104148, Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20110032120088, Elite Scholar Program of Tianjin University, and Deutscher Akademischer Austauschdienst Foundation. N. D. Jin was supported by National Natural Science Foundation of China under Grant No.
41174109 and National Science and Technology Major Project of China under Grant No. 2011ZX05020-006. J. Kurths was supported by International Research Training Group (IRTG) 1740 (Deutsche Forschungsgemeinschaft).

Keywords

coupled oscillators
synchronization
complex networks
nonlinear phenomena

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10.1038/srep04783

Low-dimensional behavior of Kuramoto model with inertia in complex networks
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title = "Low-dimensional behavior of Kuramoto model with inertia in complex networks",

abstract = "Low-dimensional behavior of large systems of globally coupled oscillators has been intensively investigated since the introduction of the Ott-Antonsen ansatz. In this report, we generalize the Ott-Antonsen ansatz to second-order Kuramoto models in complex networks. With an additional inertia term, we find a low-dimensional behavior similar to the first-order Kuramoto model, derive a self-consistent equation and seek the time-dependent derivation of the order parameter. Numerical simulations are also conducted to verify our analytical results.",

keywords = "coupled oscillators, synchronization , complex networks, nonlinear phenomena",

author = "Peng Ji and Peron, {Thomas K. D. M.} and Rodrigues, {Francisco A.} and Juergen Kurths",

note = "Z. K. Gao was supported by National Natural Science Foundation of China under Grant No. 61104148, Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20110032120088, Elite Scholar Program of Tianjin University, and Deutscher Akademischer Austauschdienst Foundation. N. D. Jin was supported by National Natural Science Foundation of China under Grant No. 41174109 and National Science and Technology Major Project of China under Grant No. 2011ZX05020-006. J. Kurths was supported by International Research Training Group (IRTG) 1740 (Deutsche Forschungsgemeinschaft).",

year = "2014",

month = may,

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doi = "10.1038/srep04783",

language = "English",

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journal = "Scientific Reports",

issn = "2045-2322",

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T1 - Low-dimensional behavior of Kuramoto model with inertia in complex networks

AU - Ji, Peng

AU - Peron, Thomas K. D. M.

AU - Rodrigues, Francisco A.

AU - Kurths, Juergen

N1 - Z. K. Gao was supported by National Natural Science Foundation of China under Grant No. 61104148, Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20110032120088, Elite Scholar Program of Tianjin University, and Deutscher Akademischer Austauschdienst Foundation. N. D. Jin was supported by National Natural Science Foundation of China under Grant No. 41174109 and National Science and Technology Major Project of China under Grant No. 2011ZX05020-006. J. Kurths was supported by International Research Training Group (IRTG) 1740 (Deutsche Forschungsgemeinschaft).

PY - 2014/5/2

Y1 - 2014/5/2

N2 - Low-dimensional behavior of large systems of globally coupled oscillators has been intensively investigated since the introduction of the Ott-Antonsen ansatz. In this report, we generalize the Ott-Antonsen ansatz to second-order Kuramoto models in complex networks. With an additional inertia term, we find a low-dimensional behavior similar to the first-order Kuramoto model, derive a self-consistent equation and seek the time-dependent derivation of the order parameter. Numerical simulations are also conducted to verify our analytical results.

AB - Low-dimensional behavior of large systems of globally coupled oscillators has been intensively investigated since the introduction of the Ott-Antonsen ansatz. In this report, we generalize the Ott-Antonsen ansatz to second-order Kuramoto models in complex networks. With an additional inertia term, we find a low-dimensional behavior similar to the first-order Kuramoto model, derive a self-consistent equation and seek the time-dependent derivation of the order parameter. Numerical simulations are also conducted to verify our analytical results.

KW - coupled oscillators

KW - synchronization

KW - complex networks

KW - nonlinear phenomena

U2 - 10.1038/srep04783

DO - 10.1038/srep04783

M3 - Article

SN - 2045-2322

VL - 4

JO - Scientific Reports

JF - Scientific Reports

M1 - 4783

ER -

Low-dimensional behavior of Kuramoto model with inertia in complex networks

Abstract

Bibliographical note

Keywords

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