Researching the relationship among traffic flow three parameters based on swallowtail catastrophe model

The kick phenomena of traffic flow can be solved by taking catastrophe mathematic models to research the relationship among traffic flow three parameters. The limitation of cusp catastrophe model is remedied by swallowtail catastrophe model, and swallowtail catastrophe model is qualitatively analyzed. It is hard to set up potential function by using conventional methods. So the potential function is set up on the basic of the evolution relationship among systems. Based on a group of measured data and the result of polynomial fitting, the relationship between velocity-density, velocity-flow and flow-density are analyzed respectively. The result of theoretical analysis is conformed to the practical condition. Because of measured data, which is detailed, it is workable to analyze these kind problems by using the method.