## 4 Simulation Results and Analysis
### Crowd Density  
Crowd density inside the carriage varies at different times of the day. During peak hours, the crowd density significantly increases, while it decreases during off-peak hours. Considering that the A-type train has a rated capacity of 310 passengers, we set the number of passengers to \(N=60\), \(N=180\), and \(N=300\), while keeping other parameters constant: \(P=0.5\), _arrival-tick_ = 100, and an even distribution of the three personality traits, each making up \(1/3\) of the total. It was assumed that no intervention was made by the authorities, with \(R=0\). We observed the proportions of passengers in four emotional states (the number of passengers in a specific emotional state/\(N\)) within the group, as shown in Figure 4.  
When _tick_\(\leq 100\) (i.e., while the train is in motion), in different crowd density scenarios, the proportions of passengers in the four emotional states undergo rapid and significant changes within a short period after departure, quickly stabilizing into a clear distribution pattern. This illustrates the explosive nature of emotional contagion. Following this initial shift, the proportions of these emotional states fluctuate within a certain range. As crowd density increases, these fluctuations lessen, indicating that higher crowd densities positively contribute to the emotional stabilization of the group. The denser the crowd, the more stable the emotional states within the group tend to be. Previous studies have also confirmed the positive influence of crowd density in facilitating the convergence of passengers' viewpoints on rumors [51]. Further analysis shows that the proportion of passengers in a calm state exhibits an almost linear decrease from _tick_ = 0 to _tick_ = 1, rapidly falling from approximately 0.1 to 0. This is attributed to the presence of a few uninformed passengers at the onset of an emergency. However, under the effects of emotional contagion, panic quickly spreads throughout the carriage, prompting these passengers to swiftly shift from a calm to a panicked state. Concurrently, the percentage of passengers in slight panic decreases, while those in moderate and intense panic states rise, particularly in the intense panic state. In Figure 4a, the moderate panic state dominates the crowd's emotions, with approximately 65% of passengers in this state. The proportion of passengers in intense panic initially decreases sharply over a short period, then begins to rise and shows oscillations. This pattern emerges because, in settings with lower crowd densities, passengers are more spread out within the carriage and are unable to promptly communicate with nearby passengers after being stimulated by a sudden event. As the initial emotional stimulus weakens, passengers' emotions gradually shift from intense to moderate and slight panic. Nonetheless, as the passengers' frantic search behavior persists, panic emotions build up, leading to a gradual increase in the proportion of passengers in intense panic. In Figure 4b, the moderate panic state remains predominant, although the proportion of passengers in this state has declined compared to the \(N\) = 60 scenario, now accounting for approximately 50%. Throughout the emotional contagion process, the proportions of passengers in both moderate and intense panic states have increased overall. Notably, the proportion of passengers in intense panic has risen significantly, indicating that the panic among passengers in the carriage is severe. In Figure 4c, the proportion of passengers experiencing intense panic rises sharply in a short period, soon matching the proportion of passengers in moderate panic. Together, passengers in these two emotional states make up approximately 90% of the total. Subsequently, intense and moderate panic levels display a  
Figure 4: Emotional state proportions of passengers under different crowd density scenarios: (**a**) \(N\) = 60; (**b**) \(N\) = 180; (**c**) \(N\) = 300.  
trend of alternating fluctuations.