Search Results (6)

Modeling cascading failure in an urban rail transit network (URTN) is essential for evaluating the impact of interruptions and network resilience. Here, a weighted coupled map lattice (CML) model is proposed. This model combines structural network coupling and passenger flow coupling to analyze the cascading failure process triggered by a station failure. Four network performance indicators are developed: network efficiency and subgraph connectivity from the network structure perspective, and OD connectivity and the reciprocal of average transfers from the network service perspective. The resilience of a URTN is measured based on the network performance indicators during station failures. Application of the model to the Wuhan URTN showed that station failure with high numbers of boarding and alighting passengers caused the highest decline in network resilience. The network’s structural resilience was stronger than its service resilience. The relationship between the percentage of failed stations and network performance indicated a significant threshold effect at a 5% failure percentage. Specifically, network performance decreased rapidly when the percentage of failed stations was below 5% and more gradually when it exceeded this threshold. Moreover, network performance exhibited high sensitivity to increases in external perturbation intensity when the failure station percentage was below 5%, but this sensitivity diminished significantly once the percentage surpassed 5%. Full article

In this paper, we aim to solve the issue of pattern formation mechanisms in a spatiotemporally discrete activator–inhibitor model that incorporates self- and cross-diffusions. We seek to identify the conditions that lead to the emergence of complex patterns and to elucidate the principles governing the dynamic behaviors that result in these patterns. We first construct a corresponding coupled map lattice (CML) model based on the continuous activator–inhibitor reaction–diffusion system. In the reaction stage, we examine the existence, uniqueness, and stability of the homogeneous stationary state and specify the parametric conditions for realizing these properties. Furthermore, by applying the center manifold theorem, we perform a flip bifurcation analysis and confirm that the model is capable of undergoing flip bifurcation. In the diffusion stage, we focus on the analysis of Turing bifurcation and determine the parameter conditions for the emergence of Turing instability. Through numerical simulations, we validate and explain the results of our theoretical analysis. Our study reveals various Turing instability mechanisms by coupling Turing and flip bifurcations, which include pure-self-diffusion-Turing instability, pure-cross-diffusion-Turing instability, flip-self-diffusion-Turing instability, flip-cross-diffusion-Turing instability, and chaos-self-diffusion-Turing instability mechanisms. Under different mechanisms, we illustrate the corresponding Turing patterns and discover a rich variety of pattern types such as labyrinthine, mosaic, alternating mosaic, colorful mottled grid patterns with winding and twisted bands, and patterns with dense patches and twisted bands nested together. Our research provides a theoretical framework and numerical support for understanding the complex dynamical behaviors and pattern formations in activator–inhibitor models with self- and cross-diffusions. Full article

The increasing frequency of urban flooding, driven by global climate change, poses significant threats to the safety and resilience of urban rail transit systems. This study systematically examines the cascading failure processes and resilience of these networks under flood conditions, with a specific focus on the Shanghai Metro. A comprehensive resilience evaluation model was developed by integrating geographic information, static network characteristics, and dynamic passenger flow indicators. This study employs an improved Coupled Map Lattice (CML) model to simulate cascading failures by considering the coupling effects of station centrality, geographic elevation, and passenger flow dynamics. The results indicate that stations with higher degrees of centrality are more likely to trigger rapid cascading failures across the network. However, incorporating dynamic passenger flow and geographic elevation data helps mitigate these effects, emphasizing the need for multi-dimensional resilience strategies. The findings provide valuable insights for urban transit management, offering a scientific foundation for developing targeted disaster response strategies to enhance network resilience against floods. This study advances our understanding of the vulnerability of urban rail transit systems and offers practical guidance for improving disaster preparedness in urban transportation infrastructure. Full article

The Gierer-Meinhardt system is one of the prototypical pattern formation models. The bifurcation and pattern dynamics of a spatiotemporal discrete Gierer-Meinhardt system are investigated via the couple map lattice model (CML) method in this paper. The linear stability of the fixed points to such spatiotemporal discrete system is analyzed by stability theory. By using the bifurcation theory, the center manifold theory and the Turing instability theory, the Turing instability conditions in flip bifurcation and Neimark–Sacker bifurcation are considered, respectively. To illustrate the above theoretical results, numerical simulations are carried out, such as bifurcation diagram, maximum Lyapunov exponents, phase orbits, and pattern formations. Full article

Analysis of the robustness and vulnerability of metro networks has great implications for public transport planning and emergency management, particularly considering passengers’ dynamic behaviors. This paper presents an improved coupled map lattices (CMLs) model based on graph attention networks (GAT) to study the cascading failure process of metro networks. The proposed model is applied to the Shanghai metro network using the automated fare collection (AFC) data, and the passengers’ dynamic behaviors are simulated by GAT. The quantitative cascading failure analysis shows that Shanghai metro network is robust to random attacks, but fragile to intentional attacks. Moreover, there is an approximately normal distribution between instant cascading failure speed and time step and the perturbation in a station which leads to steady state is approximately a constant. The result shows that a station surrounded by other densely distributed stations can trigger cascading failure faster and the cascading failure triggered by low-level accidents will spread in a short time and disappear quickly. This study provides an effective reference for dynamic safety evaluation and emergency management in metro networks. Full article

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. Full article