Analysis Of Crowd JAM In Public Buildings Based On Cusp-Catastrophe Theory

Published data on crowd accidents in public buildings show that most crowd accidents are trampling. The direct and basic reason of trampling is crowd jam. Therefore studying the crowd evacuation in modern complex buildings should involve the study of the movement of a large number of people and the mechanism of crowd jam.Current researches on the movement of a large crowd are based on the partial differential equation (PDE) model. The partial differential equation model is established based on the physical movement of the continuous crowd states. It has a strong dependence on the initial conditions. In addition, some characteristics of large crowd like the phenomena of discontinuous jumping in reality are hard to explain by partial differential equations (PDEs). For the defects in the current study, this study attempts to study the movement mechanism of crowd jam applied the catastrophe theory.In this paper, a cusp-catastrophe model is presented based on the non-linear relationship between the crowd density and movement velocity. The model combines the three-parameter model of crowd flow and cusp-catastrophe mathematical model. The paper studies the movement mechanism of crowd jam in a 1-D space. The critical density and the critical velocity of a crowd flow can be calculated through the catastrophe model. Results of the analysis indicate that (1) the catastrophe model based on complex systems cannot only describe the phenomena of non-continuity in crowds, but also obtain the critical density and the critical velocity; (2) the catastrophe model does not require initial conditions, besides the problem solving process does not involve the time and location. This means the applicability of the catastrophe model can be used more broadly than PDE model, especially the study of complex systems; (3) the catastrophe model can forecast and control the jamming state by monitoring and adjusting the variables in practice. The model supports the decision of the management of emergency evacuation.The results of the research can help safety managers evacuate the large crowd in public buildings reasonably and effectively. The results are also useful to the layout of the public building space.