Sandpile avalanche dynamics on scale-free networks

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≤ η < 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 - 2η)/(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.