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

UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84951737576&partnerID=MN8TOARS

U2 - 10.1103/PhysRevE.92.062808

DO - 10.1103/PhysRevE.92.062808

M3 - Article

SN - 1539-3755

VL - 92

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

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

IS - 6

M1 - 062808

ER -