Cascading Failures and Vulnerability Evolution in Bus⁻Metro Complex Bilayer Networks under Rainstorm Weather Conditions.

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In recent years, the frequent occurrence of rainstorms has seriously affected urban–public transport systems. In this study, we examined the impact of rainstorms on the vulnerability of urban–public transport systems consisting of both ground bus and metro systems, which was abstracted into an undirected weighted Bus–Metro complex bilayer network (Bus–Metro CBN) and the passenger volume was regarded as its weight. Through the changes in the node scale, network efficiency, and passenger volume in the maximal connected component of the Bus–Metro CBN, we constructed a vulnerability operator to quantitatively calculate the vulnerability of the Bus–Metro CBN. Then, the flow-based couple map lattices (CMLs) model was proposed to simulate cascading failure scenarios of the Bus–Metro CBN under rainstorm conditions, in which the rainstorm is introduced through a perturbation variable. The simulation results show that under the condition of passenger flow overload, the network may have a two-stage cascading failure process. The impact analysis shows that there is a rainstorm intensity threshold that causes the Bus–Metro CBN to collapse. Meanwhile, we obtained the optimal node and edge capacity through capacity analysis. In addition, our analysis implies that the vulnerability of the Bus–Metro CBN network in most scenarios is mainly caused by the degradation of network structure rather than the loss of passenger flow. The network coupling strength analysis results show that the node coupling strength has greater potential to reduce the vulnerability than edge coupling strength. This indicates that traffic managers should prioritize controlling the mutual influence between bus stops (or metro stations) to reduce the vulnerability of the Bus–Metro CBN more effectively.