中文摘要：

针对偏微分方程模型对初始条件有很强的依赖性，且不能反映拥挤人群的非连续性现象，应用突变理论分析人群拥挤现象的形成机理。建立了拥挤人群的尖点突变模型，并推导出人群拥挤状态的临界密度和临界速率。研究表明，基于复杂系统的突变模型不但能描述人群状态的非连续性现象，而且更能针对性地求出人群状态突变的临界密度和临界速率；突变模型在实践中可以通过对变量的监测和调整，实现拥挤人群状态的预测和控制。由于突变模型对初始条件没有要求，因而更符合现实情景。

英文摘要：

The paper intends to present a eatastrophe model for analyzing the phenomena that large crowds would be squeezed and turned into a jam. As is known, the PDE model is established based on the physical movement of the continuous squeezing state, though it is hard to use it to explain the phenomena of discontinuous jumping. Starting from the above necessity, this. paper has developed a cusp catastrophe model in a I-D space based on the catastrophe theory and the non-linear relationship between the crowd density and the movement velocity. The above said model is composed of the potential function, the catastrophe manifold and the bifurcation set. In this paper, we prefer to use it to analyze the mechanism of a large crowd jam by making simple graphs for a cusp catastrophe model of the crowd, the bifurcation set and the projection of catastrophe ;model, from which the critical density and the critical velocity can be gained without the initial and boundary conditions into account. Comparing the PDE model with the cusp catastrophe model, we can deduce a catastrophe model based on the complex systems for wider application. Since the cusp catastrophe model is better suited for practical application than the PDE model based on the physical movement, it can be predicted to be able to control the crowds by monitoring and adjusting the control variable in practice for its control variables. It is this coneluded that the catastrophe model introduced here is useful for analyzing the catastrophic feature of the crowd jam in the evacuation process. The model also provides a decision-making for the emergency evacuation and the large scale public building design. From the above illustration, it can be seen that the catastrophe model is indeed of significant value for the governmental departments to regulate large crowds to avoid any crowd jam.