Resilience Evaluation of Complex Networks with Attack Intensity

Both random and targeted attack behaviors were always treated as nodes or links removal in the research of traditional network robustness. However, what happens more frequently is partial failure rather than entire removal in the networks. Here, incorporated the concept of function degeneration into two attack strategies high-degree nodes (HD) and low-degree nodes (LD) with attack intensity, we explore the resilience of complex networks with dynamical behaviors against failure spreading for Scale-Free (SF) networks. With the mean-field theory, we deduce the theoretical solution between critical fraction of attacked nodes fc and attack intensity q when network loses its stability once be attacked by intensity q. We test the simulation experiments to verify the accuracy of proposed theoretical solutions. What we study actually creates a richer way for exploring the network resilience degradation with a more general attack behavior.