Dynamic Disturbance Propagation Model of Pedestrian Panic Behaviors and Lyapunov-Based Crowd Stability Analysis

In public places, pedestrian panic behaviors have received increasing attention due to their dangerous impact on normal pedestrian flow. To address this issue, this study considered crowd panic behaviors as two-dimensional Gaussian disturbances quantitatively triggered by accidents and analyzed the stability of the pedestrian crowd based on Lyapunov criterion. First, this study established a two-dimensional static model for the disturbance pressure in a crowd. Then, a dynamic disturbance-propagation model (DPM) of crowd panic behaviors was proposed based on the conservation law of fluid dynamics. The anisotropy of the disturbance pressure propagation was proven with theoretical derivations and simulation experiments, which kept consistent with ground truth. Further, a stability criterion was proposed for pedestrian crowd flow under disturbances based on Lyapunov theory. To validate the proposed DPM, we simulated a disturbance scenario in the waiting hall of Shanghai Hongqiao Railway Station. Subsequently, the visual disturbance propagation dynamics and crowd state evolution due to a panic behavior disturbance in a pedestrian crowd were investigated; Finally, the experimental results demonstrated that disturbance pressures and pedestrian density fluctuated and diffused with the panic behavior outbreak point as the disturbance center, showing heterogeneous characteristics. This study shows how we can locate the high-risk areas affected by pedestrian panic behaviors in advance, and further help control crowd flow to keep a pedestrian crowd safe in public buildings.