Sandpile avalanche dynamics on scale-free networks

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 gamma through the Bak-Tang-Wiesenfeld (BTW) sandpile model. The threshold height of a node i is set as k(i)(1-n) with 0 less than or equal to eta < 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 tau and delta, respectively. They are given as tau=(gamma-2eta)/(y-1-eta) and delta = (gamma-1-eta)/(gamma-2) for gamma < 3 - eta, 3/2 and 2 for gamma > 3 - eta, respectively. The power-law distributions are modified by a logarithmic correction at gamma = 3 - eta. (C) 2004 Elsevier B.V. All rights reserved.