## Abstract

Avalanche dynamics is an indispensable feature of complex systems. Here, we study the self-organized critical dynamics of avalanches on scale-free networks with degree exponent γ through the Bak-Tang-Wiesenfeld (BTW) sandpile model. The threshold height of a node i is set as k_{i} ^{1-η} with 0≤ η < 1, where k_{i} is the degree of node i. Using the branching process approach, we obtain the avalanche size and the duration distribution of sand toppling, which follow power-laws with exponents τ and δ, respectively. They are given as τ=(γ - 2η)/(γ - 1 - η) and δ=(γ - 1 - η)/(γ - 2) for γ < 3- η, 3/2 and 2 for γ > 3 - η, respectively. The power-law distributions are modified by a logarithmic correction at γ = 3 - η.

Original language | English |
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Pages (from-to) | 84-91 |

Number of pages | 8 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 338 |

Issue number | 1-2 SPEC. ISS. |

DOIs | |

Publication status | Published - 2004 Jul 1 |

Externally published | Yes |

## Keywords

- Avalanche
- Branching process
- Scale-free network

## ASJC Scopus subject areas

- Statistics and Probability
- Condensed Matter Physics