论文部分内容阅读
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。
The partial differential equation model has a strong dependence on the initial conditions, and can not reflect the phenomenon of crowding population discontinuities, the application of catastrophe theory to analyze the formation mechanism of crowd crowding phenomenon. The cusp catastrophe model of crowded population is established and the critical density and critical rate of population crowding state are deduced. The research shows that the catastrophe model based on complex system can not only describe the discontinuity of population status, but also find out the critical density and critical rate of crowd state mutation in a targeted manner. In practice, the mutation model can be used to monitor the variables Adjust and forecast crowded crowd status and control. Since the mutation model does not require initial conditions, it is more realistic.