基于最大Lyapunov指数改进算法的交通流混沌判别

Identification of Chaos in the Traffic Flow based on the Improved Largest Lyapunov Exponents Algorithm

提出了一种快速判别交通流混沌的最大Lyapunov指数改进算法.该算法首先用关联积分法(C-C方法)和C ao方法确定重构相空间的两个重要参数:嵌入维数m和延迟时间,再用小数据量方法计算时间序列的最大Lyapunov指数.这种算法不仅能够很好地重构原始时间序列的特性,并且能够避免W o lf方法的局限性.应用最大Lyapunov指数改进算法对仿真交通流和实测交通流的时间序列进行了混沌判别,结果表明,基于跟驰模型的仿真交通流和实际交通流中存在混沌现象,最大Lyapunov指数改进算法是准确判定时间序列是否具有混沌特性的一种有效方法.

An improved largest Lyapunov exponents＇ algorithm is put forward for rapid identificanon of chaos in traffic flow. First, the improved algorithm uses correlation integral method （C-C method） and Cao method to estimate two important variances of phase space reconstruction： embedding dimension m and delay time, then, uses small data sets to calculate the largest Lyapunov exponent from the time series. It can not only reconstruct characteristics of original data, but also avoid the limitation of the Wolf algorithm. In this case, the improved largest Lyapunov exponents＇ algorithm is used for the identification of chaos in time series of the simulated traffic flow based on car-following model and real traffic flow. The results indicate that there is chaos in the simulated traffic flow based on car-following model and real traffic flow, and the improved largest Lyapunov exponents＇ algorithm is one of the effective methods to identify the chaos in the time series exactly.