Journal
PHYSICAL REVIEW LETTERS
Volume 91, Issue 14, Pages -Publisher
AMERICAN PHYSICAL SOC
DOI: 10.1103/PhysRevLett.91.148701
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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/(gamma-1) and z=(gamma-1)/(gamma-2) in the range 2<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.
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