Application of singular perturbation method in analyzing traffic density waves  

作　　者：沈飞英 葛红霞 雷丽 

机构地区：[1]Faculty of Science,Ningbo University [2]School of Energy and Power Engineering,Shandong University

出　　处：《Journal of Shanghai University(English Edition)》2009年第1期6-11,共6页上海大学学报（英文版）

基　　金：supported by the National Basic Research Program of China (Grant No.2006CB705500);the National Natural Science Foundation of China (Grant Nos.10532060, 10602025, 10802042);the Natural Science Foundation of Ningbo (Grant No.2007A610050)

摘　　要：Car following model is one of microscopic models for describing traffic flow. Through linear stability analysis, the neutral stability lines and the critical points are obtained for the different types of car following models and two modified models. The singular perturbation method has been used to derive various nonlinear wave equations, such as the Kortewegde-Vries （KdV） equation and the modified Korteweg-de-Vries （mKdV） equation, which could describe different density waves occurring in traffic flows under certain conditions. These density waves are mainly employed to depict the formation of traffic jams in the congested traffic flow. The general soliton solutions are given for the different types of car following models, and the results have been used to the modified models efficiently.Car following model is one of microscopic models for describing traffic flow. Through linear stability analysis, the neutral stability lines and the critical points are obtained for the different types of car following models and two modified models. The singular perturbation method has been used to derive various nonlinear wave equations, such as the Kortewegde-Vries （KdV） equation and the modified Korteweg-de-Vries （mKdV） equation, which could describe different density waves occurring in traffic flows under certain conditions. These density waves are mainly employed to depict the formation of traffic jams in the congested traffic flow. The general soliton solutions are given for the different types of car following models, and the results have been used to the modified models efficiently.

关 键 词：traffic flow singular perturbation method car following models Korteweg-de-Vries （KdV） equations modified Korteweg-de-Vries （mKdV） equations 

分 类 号：O175[理学—数学] U491.113[理学—基础数学]