## Abstract

We investigate the avalanche dynamics of the Bak-Tang-Wiesenfeld sandpile model on scale-free (SF) networks, where the threshold height of each node is distributed heterogeneously, given as its own degree. We find that the avalanche size distribution follows a power law with an exponent [Formula presented]. Applying the theory of the multiplicative branching process, we obtain the exponent [Formula presented] and the dynamic exponent [Formula presented] as a function of the degree exponent [Formula presented] of SF networks as [Formula presented] and [Formula presented] in the range [Formula presented] and the mean-field values [Formula presented] and [Formula presented] for [Formula presented], with a logarithmic correction at [Formula presented]. The analytic solution supports our numerical simulation results. We also consider the case of a uniform threshold, finding that the two exponents reduce to the mean-field ones.

Original language | English |
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Journal | Physical review letters |

Volume | 91 |

Issue number | 14 |

DOIs | |

Publication status | Published - 2003 |

Externally published | Yes |

## ASJC Scopus subject areas

- Physics and Astronomy(all)