A MODEL FOR CASCADING FAILURES IN COMPLEX NETWORKS WITH A TUNABLE PARAMETER

In this paper, based on the local preferential redistribution rule of the load after removing a node, we propose a cascading model and explore cascading failures on four typical networks , i.e. the BA with scale-free property, the WS small-world network, the NW network and the ER random network. Assume that a failed node leads only to are distribution of the load passing through it to its neighboring nodes. We find that all networks reach the strongest robustness level against cascading failures in the case of alpha=1, which is a tunable parameter in our model, where the robustness is quantified by the critical threshold T-c, at which a phase transition occurs from a normal state to collapse. To a constant network size, we further discuss the correlations between the average degree < k > and T-c, and draw the conclusion that T-c has a negative correlative with < k >, i.e. the bigger the value of < k >, the smaller the critical threshold T-c. These results may b every helpful for real-life networks to avoid cascading-failure-induced disasters.