Sandpile avalanche dynamics on scale-free networks

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 $γ$ through the Bak-Tang-Wiesenfeld (BTW) sandpile model. The threshold height of a node $i$ is set as $k_i^{1-η}$ with $0\leqη<1$, 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 $τ$ and $δ$, respectively. They are given as $τ=(γ-2 η)/(γ-1-η)$ and $δ=(γ-1-η)/(γ-2)$ for $γ<3-η$, 3/2 and 2 for $γ>3-η$, respectively. The power-law distributions are modified by a logarithmic correction at $γ=3-η$.