Cascading toppling dynamics on scale-free networks

We study avalanche dynamics on scale-free networks, following a power-law degree distribution, pd(k)∼k-γ, through the Bak–Tang–Wiesenfeld sandpile model. The threshold height of a node i is set to be ki1-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.