Dynamical resilience of networks against targeted attack

To mitigate the damage caused by external interference, many researchers have studied the resilience changes in network when it is under targeted attack. However, it is still unclear how dynamical processes impact network resilience. Here, with a broad range of steady-state dynamical processes including birth-death processes ( BD), regulatory dynamics (R) and epidemic processes (E) on Scale-Free (SF) and Erdős–Rényi (ER) networks, we explore the resilience of complex networks under two attack strategies: from high-degree nodes (HD) and from low-degree nodes (LD). Mapping the multi-dimensional dynamics equation into one-dimensional equation, we quantify the relationship between network resilience and attacked node fraction f and present the critical thresholds f_c at which the network loses its resilience. When take dynamical processes into consideration in resilience research, we get some novel conclusions. Compared to structural robustness without dynamical processes, with R or E, ER networks are more vulnerable and the heterogeneity of SF networks has different effects on thresholds f_c under HD attack strategy. The theoretical solutions are consistent with the simulation results to some extent, our outcomes are helpful for optimizing networks and enhancing the resilience of networks.