TY - JOUR

T1 - Sandpile on scale-free networks

AU - Goh, K. I.

AU - Lee, D. S.

AU - Kahng, B.

AU - Kim, D.

N1 - Funding Information:
This work is supported by the KOSEF Grant No. R14-2002-059-01000-0 in the ABRL program.

PY - 2003

Y1 - 2003

N2 - 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 [Formula presented]. Applying the theory of the multiplicative branching process, we obtain the exponent [Formula presented] and the dynamic exponent [Formula presented] as a function of the degree exponent [Formula presented] of SF networks as [Formula presented] and [Formula presented] in the range [Formula presented] and the mean-field values [Formula presented] and [Formula presented] for [Formula presented], with a logarithmic correction at [Formula presented]. 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.

AB - 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 [Formula presented]. Applying the theory of the multiplicative branching process, we obtain the exponent [Formula presented] and the dynamic exponent [Formula presented] as a function of the degree exponent [Formula presented] of SF networks as [Formula presented] and [Formula presented] in the range [Formula presented] and the mean-field values [Formula presented] and [Formula presented] for [Formula presented], with a logarithmic correction at [Formula presented]. 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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U2 - 10.1103/PhysRevLett.91.148701

DO - 10.1103/PhysRevLett.91.148701

M3 - Article

AN - SCOPUS:0242425251

VL - 91

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 14

ER -