### Abstract

Original language | English |
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Article number | 062808 |

Journal | Physical Review. E, Statistical, Nonlinear and Soft Matter Physics |

Volume | 92 |

Issue number | 6 |

DOIs | |

Publication status | Published - 8 Dec 2015 |

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### 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.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Approximate solution for frequency synchronization in a finite-size Kuramoto model

AU - Wang, Chengwei

AU - Rubido, Nicolas

AU - Grebogi, Celso

AU - Baptista, Murilo S.

PY - 2015/12/8

Y1 - 2015/12/8

N2 - 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.

AB - 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.

KW - nlin.AO

U2 - 10.1103/PhysRevE.92.062808

DO - 10.1103/PhysRevE.92.062808

M3 - Article

VL - 92

JO - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics

JF - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics

SN - 1539-3755

IS - 6

M1 - 062808

ER -