Probabilistic analysis of cascade failure dynamics in complex network

The impact of initial load and tolerance parameter distribution on cascade failure is investigated. By using mean field theory, a probabilistic cascade failure model is established. Based on the model, the damage caused by certain attack size can be predicted, and the critical attack size is derived by the condition of cascade failure end, which ensures no collapse. The critical attack size is larger than the case of constant tolerance parameter for network of random distribution. Comparing three typical distributions, simulation results indicate that the network whose initial load and tolerance parameter both follow Weibull distribution performs better than others.