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 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−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.