Sandpile avalanche dynamics on scale-free networks

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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 kᵢ¹⁻η with 0≤η<1, where kᵢ 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.