## 2 Methods
### Emotional Computation  
We define an individual's emotional level as a combination of two components: (1) the initial cognitive appraisal of the environment and (2) the subsequent instinctive, unconscious emotional contagion [42]. Before delving into the details of cognitive appraisal and emotional contagion, let us first clarify how emotions are generally updated. At the initial moment (\(t=0\)), passengers' panic is entirely derived from their own cognitive appraisal. However, over time, their panic is influenced not only by their own cognitive appraisal but also by emotional contagion. Building on [PERSON]'s research [42], weight coefficients \(\rho\) and \(1-\rho\) are introduced to measure respective impacts of emotional contagion and cognitive appraisal. Based on Equation (1), we calculate the emotional level of passenger \(i\) at time \(t\) and normalize it to a value between 0 and 1:  
\[e_{i}(t)=\left\{ \begin{aligned} f_{i},t&=0\\ (1-\rho)f_{i}+\rho\lambda_{i}(t),t&=1,2,3\ldots\end{aligned} \right. \tag{1}\]  
where \(f_{i}\) is the appraisal contribution function and \(\lambda_{i}(t)\) is the contagion contribution function. Here, \(\rho\) is related to the passengers' personality traits, represented by \(pc=\{1\),\(2\),\(3\}\), where 1 indicates a sensitive type, 2 a neutral type, and 3 a conservative type [43]. The probability distribution of \(\rho\) can be expressed by \(\rho^{pc}\). Let \(\rho^{pc}=1\) be randomly distributed over [0.6, 1], \(\rho^{pc}=2\) randomly distributed over [0.4, 0.6], and \(\rho^{pc}=3\) randomly distributed over [0, 0.4]. As the passenger's personality trait shifts from sensitive (\(pc=1\)) to neutral (\(pc=2\)) and, finally, to conservative (\(pc=3\)), the influence of emotional contagion on the passenger gradually diminishes, while the impact of cognitive appraisal grows stronger. When metro emergencies occur, they are often accompanied by visual or auditory sensory stimuli. As passengers assess their surroundings, these external stimuli can trigger feelings of panic. According to the Weber-Fechner Law, which is expressed as \(S=K\lg(R)\), a formula for calculating the individual's cognitive appraisal of the environment is proposed as follows:  
\[f_{i}=\alpha_{i}\lg(1+N_{i}(0)) \tag{2}\]  
where \(\alpha_{i}\) is defined as the emotional sensitivity [44] of passenger \(i\). The parameter \(\alpha_{i}\) is associated with the passenger's personality traits, represented by \(pc=\{1\),\(2\),\(3\}\), where 1 indicates a sensitive type, 2 a neutral type, and 3 a conservative type [43]. And it is assumed that the \(\alpha_{i}\) for a sensitive passenger is equal to 1.2, for a neutral passenger is equal to 1, and for a conservative passenger is equal to 0.8. \(N_{i}(0)\) denotes the initial intensity of environmental stimuli perceived by passenger \(i\) at the onset of an emergency. Given the mathematical properties of Equation (2), \(N_{i}(0)\) is assumed to follow a uniform distribution between 0 and 9. In an enclosed space, people instinctively mimic others' facial expressions, gestures, vocalizations, postures, and movements, synchronizing with them and ultimately achieving emotional alignment--a phenomenon known as emotional contagion. During the process of panic emotional contagion, sensory information conveyed through the expressions, speech, and actions of nearby passengers generates new sources of stimulation, leading to changes in passengers' emotions. Consequently, according to the Weber-Fechner Law, the \begin{table}
\begin{tabular}{c c} \hline
**Emotional Levels** & **Emotional States** \\ \hline
0 & Calm \\ (0, 0.4] & Slight panic \\ (0.4, 0.8] & Moderate panic \\ (0.8, 1.0] & Intense panic \\ \hline \end{tabular}
\end{table} 
Table 1: Emotional states corresponding to emotional levels. changes in the emotion of passenger \(i\) during emotional contagion process can be expressed by Equation (3):  
\[\lambda_{i}(t)=\left\{ \begin{aligned} 0,\,t=0\\ \alpha_{i}\text{lg}(1+N_{i}(t)),\,t=1,2,3\ldots\end{aligned} \right.