Cascading toppling dynamics on scale-free networks

We study avalanche dynamics on scale-free networks, following a power-law degree distribution, P-d(k-) similar to k(-gamma), through the Bak-Tang-Wiesenfeld sandpile model. The threshold height of a node i is set to be k(i)(1-eta) with 0 less than or equal to eta < 1. We obtain the exponents for the avalanche size and the duration distributions analytically as a function of gamma and eta by using the branching process approach. The analytic solution is checked with numerical simulations on both artificial uncorrelated networks such as the static model and real-world networks. While numerical results of the avalanche size distribution for artificial uncorrelated scale-free networks are in reasonable agreement with the analytic prediction, those for real-world networks are not, which may be attributed to non-trivial degree-degree correlations in real-world networks. (C) 2004 Elsevier B.V. All rights reserved.