Robustness of partially interdependent networks under combined attack.

We thoroughly study the robustness of partially interdependent networks when suffering attack combinations of random, targeted, and localized attacks. We compare analytically and numerically the robustness of partially interdependent networks with a broad range of parameters including coupling strength, attack strength, and network type. We observe the first and second order phase transition and accurately characterize the critical points for each combined attack. Generally, combined attacks show more efficient damage to interdependent networks. Besides, we find that, when robustness is measured by the critical removing ratio and the critical coupling strength, the conclusion drawn for a combined attack is not always consistent.