Crowd stability analysis based on fluid resonance superposition principle and Lyapunov criterion

Abstract

It is significant to analyze the stability of a crowd in public places to avoid possible confusion and dangerous accidents. This paper introduces fluid wave theory and regards the crowded groups as continuous media. Crowd panic propagation can be mapped into the spreading of fluid waves. In the case of emergencies, individual pedestrian’s emotion values are calculated by the panic propagation model. Based on the resonance and superposition principles of waves, this study converts emotion value into individual internal frequency. Considering the interaction between individuals, trust coefficient is defined to express the external equivalent frequency. Whether resonance occurs, with amplitude of negative emotion being amplified, can be judged through comparing the pedestrian internal frequency and the external equivalent frequency. In addition, Lyapunov criterion is applied to analyze the crowd stability from a system perspective. The flow chart of algorithm steps and implementation process are designed to realize application of wave superposition and resonance in crowd Stability. This study can further provide a more feasible program to observe the crowd in real time as well as guide evacuation decisions.