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 through the Bak–Tang–Wiesenfeld (BTW) sandpile model. The threshold height of a node i is set as k1− i with 06 ¡ 1, where ki 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 and , respectively. They are given as =( −2 )=( −1− ) and = ( − 1− )=( − 2) for ¡ 3− , 3=2 and 2 for ¿ 3− , respectively. The power-law distributions are modi5ed by a logarithmic correction at = 3− . c © 2004 Elsevier B.V. All rights reserved. PACS: 89.70.+c; 89.75.−k; 05.10.−a