Sandpile on scale-free networks

• Published in: Physical review letters Vol. 91; no. 14; p. 148701
• Main Authors: Goh, K-I, Lee, D-S, Kahng, B, Kim, D
• Format: Journal Article
• Language: English
• Published: United States 03.10.2003
• ISSN: 0031-9007
• DOI: 10.1103/PhysRevLett.91.148701

We investigate the avalanche dynamics of the Bak-Tang-Wiesenfeld sandpile model on scale-free (SF) networks, where the threshold height of each node is distributed heterogeneously, given as its own degree. We find that the avalanche size distribution follows a power law with an exponent tau. Applying the theory of the multiplicative branching process, we obtain the exponent tau and the dynamic exponent z as a function of the degree exponent gamma of SF networks as tau=gamma divided by (gamma-1) and z=(gamma-1) divided by (gamma-2) in the range 2<gamma<3 and the mean-field values tau=1.5 and z=2.0 for gamma>3, with a logarithmic correction at gamma=3. The analytic solution supports our numerical simulation results. We also consider the case of a uniform threshold, finding that the two exponents reduce to the mean-field ones.