Cascading toppling dynamics on scale-free networks

We study avalanche dynamics on scale-free networks, following a power-law degree distribution, p_d(k) ∼ k^θ, through the Bak-Tang-Wiesenfeld sandpile model. The threshold height of a node i is set to be k_i^1-η with 0≤η<1. We obtain the exponents for the avalanche size and the duration distributions analytically as a function of γ and η by using the branching process approach. The analytic solution is checked with numerical simulations on both artificial uncorrelated networks such as the static model and real-world networks. While numerical results of the avalanche size distribution for artificial uncorrelated scale-free networks are in reasonable agreement with the analytic prediction, those for real-world networks are not, which may be attributed to non-trivial degree-degree correlations in real-world networks.