Abstract: Since there exists a certain degree monitoring and control in real-life networks, not all overloaded edges will be removed from networks.We propose a mechanism of the breakdown probability of an overload edge, and construct a cascading model with the breakdown probabililty.We compare the universal cascading phenomena on BA scale-free and WS small-world networks subject to two different attacks on edges, investigate the effects of the breakdown probability and different network structures on edge attack strategies, and analyze coping strategies to prevent cascading failures.The consistency of numerical simulation and theoretical analysis also verifies the correctness of the conclusions.

Key words: cascading failure, complex network, breakdown probability, attack strategy