应用改进型小数据量法计算交通流的最大Lyapunov 指数

最大Lyapunov指数是非线性系统的一个非常重要的特征量.微观仿真交通流具有典型的非线性,计算交通流的最大Lyapunov指数对研究交通流的非线性特征具有重要意义.通过用虚假临界点法计算嵌入维数可以使小数据量法更加完善.首先应用改进型小数据量法计算几个典型的非线性系统的最大Lyapunov指数,验证算法结果的准确性.然后再用此方法首次对Bierley跟驰模型产生的微观仿真交通流和微观实测车流的时间序列进行实证分析.结果表明,该方法能较准确的计算出最大Lyapunov指数,可以作为研究交通流非线性特征的定量方法.

The Computing of Maximum Lyapunov Exponent in Traffic Flow Applying the Improved Small-data Method

The maximum lyapunov exponent is a very important measure to describe nonlinear system.Microcosmic simulation traffic flow has typical nonlinear feature.So it is important for the research on characteristic of nonlinear in traffic flow to compute maximum lyapunov exponent in traffic flow.The small-data method is improved by false nearest neighbor method calculating embedding dimension.Firstly,the maximum lyapunov exponent of several typical nonlinear systems are computed by the improved small-data method in order to confirm the veracity of results of the algorithm.Secondly,time series of microcosmic simulation traffic flows generated by Bierley model and real vehicle flow are first researched with it.The results indicate that this method can compute maximum lyapunov exponents of them exactly and can be treated as a quantitative method for study of characteristic of nonlinear in traffic flow.