### Abstract

We investigate Kuramoto dynamics on scale-free networks to include the effect of weights, as weighted networks are conceivably more pertinent to real-world situations than unweighted networks. We consider both symmetric and asymmetric coupling schemes. Our analysis and computations indicate that more links in weighted scale-free networks can either promote or suppress synchronization. In particular, we find that as a parameter characterizing the weighting scheme is varied, there can be two distinct regimes: a normal regime where more links can enhance synchronization and an abnormal regime where the opposite occurs. A striking phenomenon is that for dense networks for which the mean-field approximation is satisfied, the point separating the two regimes does not depend on the details of the network structure such as the average degree and the degree exponent. This implies the existence of a class of weighted scale-free networks for which the synchronization dynamics are invariant with respect to the network properties. We also perform a comparison study with respect to the onset of synchronization in Kuramoto networks and the synchronization stability of networks of identical oscillators.

Original language | English |
---|---|

Article number | 013134 |

Number of pages | 8 |

Journal | Chaos |

Volume | 19 |

Issue number | 1 |

DOIs | |

Publication status | Published - Mar 2009 |

### Keywords

- complex networks
- nonlinear dynamical systems
- synchronisation
- dynamical networks
- Kuramoto
- oscillators

### Cite this

*Chaos*,

*19*(1), [013134]. https://doi.org/10.1063/1.3087420

**Onset of synchronization in weighted scale-free networks.** / Wang, Wen-Xu; Huang, Liang; Lai, Ying-Cheng; Chen, Guanrong.

Research output: Contribution to journal › Article

*Chaos*, vol. 19, no. 1, 013134. https://doi.org/10.1063/1.3087420

}

TY - JOUR

T1 - Onset of synchronization in weighted scale-free networks

AU - Wang, Wen-Xu

AU - Huang, Liang

AU - Lai, Ying-Cheng

AU - Chen, Guanrong

PY - 2009/3

Y1 - 2009/3

N2 - We investigate Kuramoto dynamics on scale-free networks to include the effect of weights, as weighted networks are conceivably more pertinent to real-world situations than unweighted networks. We consider both symmetric and asymmetric coupling schemes. Our analysis and computations indicate that more links in weighted scale-free networks can either promote or suppress synchronization. In particular, we find that as a parameter characterizing the weighting scheme is varied, there can be two distinct regimes: a normal regime where more links can enhance synchronization and an abnormal regime where the opposite occurs. A striking phenomenon is that for dense networks for which the mean-field approximation is satisfied, the point separating the two regimes does not depend on the details of the network structure such as the average degree and the degree exponent. This implies the existence of a class of weighted scale-free networks for which the synchronization dynamics are invariant with respect to the network properties. We also perform a comparison study with respect to the onset of synchronization in Kuramoto networks and the synchronization stability of networks of identical oscillators.

AB - We investigate Kuramoto dynamics on scale-free networks to include the effect of weights, as weighted networks are conceivably more pertinent to real-world situations than unweighted networks. We consider both symmetric and asymmetric coupling schemes. Our analysis and computations indicate that more links in weighted scale-free networks can either promote or suppress synchronization. In particular, we find that as a parameter characterizing the weighting scheme is varied, there can be two distinct regimes: a normal regime where more links can enhance synchronization and an abnormal regime where the opposite occurs. A striking phenomenon is that for dense networks for which the mean-field approximation is satisfied, the point separating the two regimes does not depend on the details of the network structure such as the average degree and the degree exponent. This implies the existence of a class of weighted scale-free networks for which the synchronization dynamics are invariant with respect to the network properties. We also perform a comparison study with respect to the onset of synchronization in Kuramoto networks and the synchronization stability of networks of identical oscillators.

KW - complex networks

KW - nonlinear dynamical systems

KW - synchronisation

KW - dynamical networks

KW - Kuramoto

KW - oscillators

U2 - 10.1063/1.3087420

DO - 10.1063/1.3087420

M3 - Article

VL - 19

JO - Chaos

JF - Chaos

SN - 1054-1500

IS - 1

M1 - 013134

ER -