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 . Applying the theory of the multiplicative branching process, we obtain the exponent and the dynamic exponent as a function of the degree exponent of SF networks as and in the range and the mean-field values and for , with a logarithmic correction at . 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.
- Received 11 May 2003
DOI:https://doi.org/10.1103/PhysRevLett.91.148701
©2003 American Physical Society