Cascading failure spreading on weighted heterogeneous networks

Abstract

We study the onset and spreading of cascading failure on weighted heterogeneous networks by adopting a local weighted flow redistribution rule, where the weight and tolerance of a node is correlated with its link degree k as kθ and Ckθ, respectively. The weight parameter θ and tolerance parameter C are positive: θ>0 and C>1.0. Assume that a failed node leads only to a redistribution of flow passing through it to its nearest-neighboring nodes. We give our theoretical estimations of the onset of the cascading failure for different values of θ. We also explore the statistical characteristics of the avalanche size on the networks by varying θ and obtain versatile dynamical scenarios of the cascading processes, which exhibit either 'subcritical', or 'critical', or 'supercritical' behaviors, depending on the value of the weight parameter. Moreover, we investigate the effect of degree correlation on the cascading failure spreading on weighted scale-free networks. It is found that single failure on assortative scale-free networks may be more likely to induce a series of subsequent failure events up to a large scale, and the cascading dynamics may easily self-organize to a 'criticality' state on such assortative scale-free networks.