# Vulnerability Analysis of the China Railway Express Network Under Emergency Scenarios
## 2 Literature Review
### Research on the Network Vulnerability  
Network vulnerability research aims to elucidate how complex networks respond to various disturbances and attacks, particularly focusing on cascading failure mechanisms and dynamic fault propagation. The small-world network model introduced by [PERSON] and [PERSON] (1998) provides a new perspective on understanding network vulnerability in the face of localized failures. Their research emphasizes the crucial role of network connectivity in influencing cascading failure outcomes [10]. Subsequent studies by [PERSON] et al. (2000) and [PERSON] et al. (2000) explored how different topological features affect a network's fault resilience, highlighting the relationship between the node degree distribution and overall network vulnerability [11; 12]. [PERSON] et al. (2003) expanded our understanding of scale-free networks by analyzing the impact of various attack strategies on network vulnerability [13].  
Although these studies offer a broad view of network vulnerability, conventional vulnerability analysis methods may be insufficient for complex networks with unique structures and operational modes, such as those found in the CR Express. Given that these trains rely heavily on specific transportation channels and hubs, their distinct operational mode and structural characteristics require more nuanced analytical tools. Traditional methodologies often focus on static network structures and single failure modes, potentially missing the vulnerability of networks with complex dynamic behaviors, such as the CR Express. For example, traditional analyses might not fully capture the network's dynamic responses and cascading effects during multiple sudden events.  
To address this gap, this paper utilizes the Coupled Map Lattice (CML) model to describe the cascading failure phenomena observed in CR Express operations. As a spatiotemporal dynamic model, CML effectively captures intricate dynamic behaviors and fault propagation mechanisms within networks [14; 15; 16]. Previous research has applied the CML model to various network types for vulnerability analysis. For example, [PERSON] and [PERSON] (2013) compared the cascading behavior of rail transit networks in Beijing, Shanghai, and Guangzhou [17]. [PERSON] (2015) used CML to refine a complex multi-link bus network model, examining cascading failures under varying external disturbances and coupling strengths [18]. [PERSON] (2018) introduced a weighted rail transit network cascading failure analysis model based on CML, focusing on the vulnerability of Beijing's weighted rail transit network [19]. [PERSON] (2022) examined the evolution of chain failures in rail transit networks, presenting an enhanced CML model that highlights how station risk resistance and geographical positioning affect fault propagation [20].  
In summary, the current research primarily focuses on the operational optimization of the CR Express and foundational network vulnerability analysis. However, the impact of network node failures, edge disruptions, and cargo flow redistribution due to unexpected events remains underexplored. This paper aims to systematically analyze the vulnerability of the CRN in response to sudden events using the CML model, with particular attention being paid to the effects of node failures, edge disruptions, and cargo flow reallocation on network cascading failures. This approach provides a novel theoretical foundation and practical guidance for enhancing the network's risk resilience.