Approximate solution for frequency synchronization in a finite-size Kuramoto model

Chengwei Wang, Nicolas Rubido, Celso Grebogi, Murilo S. Baptista

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Abstract

Scientists have been considering the Kuramoto model to understand the mechanism behind the appearance of collective behavior, such as frequency synchronization (FS) as a paradigm, in real-world networks with a finite number of oscillators. A major current challenge is to obtain an analytical solution for the phase angles. Here, we provide an approximate analytical solution for this problem by deriving a master solution for the finite-size Kuramoto model, with arbitrary finite-variance distribution of the natural frequencies of the oscillators. The master solution embodies all particular solutions of the finite-size Kuramoto model for any frequency distribution and coupling strength larger than the critical one. Furthermore, we present a criterion to determine the stability of the FS solution. This allows one to analytically infer the relationship between the physical parameters and the stable behavior of networks.
Original languageEnglish
Article number062808
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Volume92
Issue number6
DOIs
Publication statusPublished - 8 Dec 2015

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frequency synchronization
Kuramoto Model
Approximate Solution
Synchronization
Analytical Solution
oscillators
Collective Behavior
Particular Solution
frequency distribution
Natural Frequency
resonant frequencies
phase shift
Paradigm
Angle
Arbitrary

Keywords

  • nlin.AO

Cite this

Approximate solution for frequency synchronization in a finite-size Kuramoto model. / Wang, Chengwei; Rubido, Nicolas; Grebogi, Celso; Baptista, Murilo S.

In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, Vol. 92, No. 6, 062808 , 08.12.2015.

Research output: Contribution to journalArticle

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