Acceleration-critical density time-delay model for crowd stability analysis based on Lyapunov theory

Rongyong Zhao,Yunlong Ma,Ping Jia,Cuiling Li,Zhishu Zhang,Yan Wang,J Zhu

doi:10.1051/matecconf/202235503019

Abstract

Crowd stability analysis is one of research hotspots to alleviate the severe situation of stampede accidents worldwide. Different from the conventional analysis models for crowd stability based on pedestrian density, this study analyses the characteristics of external disturbances and internal obstacle disturbance based on Lyapunov's theory. The critical range of crowd acceleration in crowd evacuation is obtained, a crowd merging acceleration-critical density time delay model is established, and a stability criterion of acceleration vector based on Lyapunov is obtained based on Lyapunov stability analysis. This provides new information for ensuring the stability of crowd movement in public places, assessing the stability of the crowd in the area, and taking reasonable protection and guidance measures prior to instability of a crowd flow.

Highlights

Serious pedestrian accidents occurred frequently in the past decade
The crowd density in a specific area in public places can reflect the stability of the crowd to a large extent, that is, the crowd density can be used as an indicator of crowd stability [1]
Different from the conventional analysis models above, this study analyzes the characteristics of external disturbances and internal obstacle disturbance based on Lyapunov's theory, proposes a crowd merging acceleration-critical density time delay model

Summary

Introduction

On June 20, 2013, Beckham visited Tongji University When he entered the stadium, the fans lost control and the stampede caused huge casualties. On December 31st, 2014, a large number of pedestrians under the observation deck of the Bund in Shanghai hedged up and down, causing 36 pedestrians to die and 49 others to be injured. These accidents around the world caused a large number of casualties and economic losses. It is important to obtain the crowd density in a specific area of public places, evaluate the stability of the crowd in this area, and take reasonable guidance measures in time before the crowd is in a state of instability. Different from the conventional analysis models above, this study analyzes the characteristics of external disturbances and internal obstacle disturbance based on Lyapunov's theory, proposes a crowd merging acceleration-critical density time delay model

The stability of crowd evacuation based on Lyapunov

The acceleration-critical density time-delay model

Summary