### 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 |
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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