Robustness of complex networks: Cascading failure mechanism by considering the characteristics of time delay and recovery strategy

To study the robustness of complex networks while encountering random failures or deliberate attacks, the cascading failure model is constructed by considering failure propagation with probability, which can depict the dynamic failure process. In particular, the characteristics of time delay and repetitive failure are taken into account in our model, and the network comprehensive robustness index (RI) is further designed according to valid survival edges and nodes. Additionally, the probability recovery strategy is proposed as well, and it is implemented in four typical networks, including the BA network, WS network, NC network and ER network. Different parameters in our model, including α, f, R, and β, are applied in simulation experiments to reveal their effects on RI in the cascading failure process. The simulation results show that nodes’ recovery abilities increase with R, which reduce the impacts of cascading failures and produce good network robustness. Meanwhile, the time delay increases with parameter α, and the size of the cascading failure decreases accordingly, which indicates that the larger that the time delay is, the stronger the RI. Additionally, the speed of the cascading failure process and the size of the cascading failure both present an increasing trend when parameter f increases gradually in the cascading failure. This indicates that the failure probability apparently impacts the RI. We also analyze the turning point t for RI(t) during the cascading failure process.