Abstract:

The dynamic analysis of cascade failure propagation paths in transportation networks remains a notable challenge in network vulnerability research. This study introduces an innovative integrated approach that combines an enhanced coupled map lattice (CML) model with Gephi 's dynamic graph analysis to identify vulnerable cascade paths and critical nodes effectively. Using Fujian Province's expressway network as a case study, the traditional CML model is enhanced by incorporating tunnel and traffic coupling factors, enabling the determination of trigger thresholds and propagation speeds of cascade failures under various attack strategies. Gephi's dynamic graph function captures the cascade failure propagation process, and we propose a "node failure tree diagram" to illustrate the temporal and sequential continuity relationships of node failures. Additionally, a "reverse-order marking method for failed nodes" is developed using a reverse-order marking and forward-order searching algorithm to identify vulnerable paths and critical nodes in failure propagation. The results demonstrate  that while all nodes exhibit some perturbation resistance (failure threshold R ≤ 1.1), robustness varies significantly (1.2 ≤ R ≤ 4.8), with an average threshold of 2.02. Among four targeted attacks—maximum node degree, betweenness, V/C ratio, and tunnel factor—attacks based on maximum betweenness and V/C ratio are most critical, reaching peak failure in 17 and 21 time-steps, respectively. Identifying critical nodes in primary and secondary vulnerable paths revealed eight key nodes, whose enhance the robustness significantly suppresses the scale of cascade propagation. This study offers a novel approach to analyzing transportation network vulnerability and supports risk-resistant network planning.

Key words: integrated transportation, cascade failure propagation, Coupled Map Lattice, fragile propagation paths, reverse-order labelling method