Cascading toppling dynamics on scale-free networks

We study avalanche dynamics on scale-free networks, following a power-law degree distribution, pd ðkÞ k ; through the Bak–Tang–Wiesenfeld sandpile model. The threshold height of a node i is set to be k 1 Z i with 0pZo1: We obtain the exponents for the avalanche size and the duration distributions analytically as a function of g and Z 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 realworld networks. r 2004 Elsevier B.V. All rights reserved. PACS: 89.70.+c; 89:75: k; 05:10: a