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 1−η i 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. Key words: avalanche, scale-free network, branching proces
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