Sandpile on scale-free networks with assortative mixing

Abstract

We numerically investigate the Bak–Tang–Wiesenfeld sandpile model on scale-free networks with assortative mixing, where the threshold height of each node is equal to its degree. It is observed that a large fraction of multiple topplings are included in avalanches on assortative networks, which is absent on uncorrelated networks. We introduce a parameter to characterize the fraction of multiple topplings in avalanches of area a. The fraction of multiple topplings increases dramatically with the degree of assortativity and has a peak for small a whose height also increase with the assortativity of the networks. Unlike the case on uncorrelated networks, the distributions of avalanche size, area and duration do not follow pure power law, but deviate more obviously from pure power law with the growing degree of assortativity. The results show that the assortative mixing has a strong influence on the behavior of avalanche dynamics on complex networks.