Sandpile avalanche dynamics on scale-free networks

Details Sandpile avalanche dynamics on scale-free networks Sandpile avalanche dynamics on scale-free networks

2004-01-27

arxiv.org/abs/cond-mat/0401531v1

Physica A 338, 84 (2004)

Physics

Condensed Matter

Statistical Mechanics

8 pages, elsart style

Scientific paper

10.1016/j.physa.2004.02.028

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 $k_i^{1-\eta}$ with $0\leq\eta<1$, where $k_i$ 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 $\gamma<3-\eta$, 3/2 and 2 for $\gamma>3-\eta$, respectively. The power-law distributions are modified by a logarithmic correction at $\gamma=3-\eta$.

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