Abstract: First，by using the individual vehicles purchasing model which based on the catastrophe theory, the paper analyses the relationship between the quantity of individual vehicles and the citizen’s average income，and in what condition will the high tide of individual vehicles purchasing take place. Then as an example，to analyses the data of Beijing’ individual vehicles purchase. Second, based on the fractal method, the paper gives a model to forecaste the quantity of Beijing’individual vehicles in three years. The paper is proved feasible by compare the forecasting result of the nearest year with the actual data.

Key words: catastrophe theory, quantity of individual vehicles, fratals, forecasting

摘要： 首先运用建立在突变理论上的汽车购买热潮分析模型，分析了私人汽车购买量与人均国民收入及交通政策之间的关系，以及在何种条件下才会出现汽车的购买高潮，并以北京市的实际数据为实例做了具体分析.然后用分形方法建立了北京私人汽车拥有量的预测模型，并预测了北京市未来三年的私人汽车拥有量，将最近一年的预测数据与实际数据做了比较，得出可行性.

关键词: 突变理论, 私人汽车拥有量, 分形, 预测