Abstract: In or der t o discuss cascading failur es on compl ex net works subject to random failures or att acks, adopting the initial load of a node j to be L_j=Bk_j^A(k_j is the degree of node j, Aand Bare tunable parameters), a cascading model with a tunable parameter is proposed based on the local preferential redist ribution rule of the load of a broken node.According to a new measure, i.e., the critical threshold T_c, we compare the effects of two at tacks for the universal robust ness.Numerical simulat ions draw some interesting and counterintuit ive results.On the one hand, the at tack at the node with the lowest degree is more likely to trigger cascading failures than the one at the highest degree nodes when A<1; while on the other hand, when A=1, the effects of two at tacks for the robustness against cascading failures are almost identical.In addition, numerical simulations are also verified by theoretical analysis.

Key words: cascading failure, complex network, critical threshold, at tack