Citation

Lee DS, Goh KI, Kahng B, Kim D. Physica A Stat. Mech. Appl. 2004; 338(1-2): 84-91.

Copyright

(Copyright © 2004, Elsevier Publishing)

DOI

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PMID

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Abstract

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 ki1-[eta] with 0[less-than-or-equals, slant][eta] lt 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 [tau] and [delta], respectively. They are given as [tau]=([gamma]-2[eta])/([gamma]-1-[eta]) and [delta]=([gamma]-1-[eta])/([gamma]-2) for [gamma] lt 3-[eta], 3/2 and 2 for [gamma] gt 3-[eta], respectively. The power-law distributions are modified by a logarithmic correction at [gamma]=3-[eta].