TDGL and mKdV equations for car-following model considering driver's anticipation

被引：29
作者：
Lv, Feng [1 ]
Zhu, Hui-Bing [2 ]
Ge, Hong-Xia [3 ]
机构：
[1] Ningbo Univ, Fac Sci, Ningbo 315211, Zhejiang, Peoples R China
[2] Ningbo Univ, Fac Architectural Civil Engn & Environm, Ningbo 315211, Zhejiang, Peoples R China
[3] Ningbo Univ, Fac Maritime & Transportat, Ningbo 315211, Zhejiang, Peoples R China
来源：
NONLINEAR DYNAMICS | 2014年 / 77卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Traffic flow; Phase transition; TDGL equation; mKdV equation; TRAFFIC FLOW; JAMMING TRANSITION; DIFFERENCE MODEL; LATTICE MODEL;
D O I：
10.1007/s11071-014-1374-5
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
Car-following models are proposed to describe the jamming transition in traffic flow on a highway. In this paper, a new car-following model considering the driver's forecast effect is investigated to describe the traffic jam. The nature of the model is studied using linear and nonlinear analysis method. A thermodynamic theory is formulated to describe the phase transition and critical phenomenon in traffic flow and the time-dependent Ginzburg-Landau (TDGL) equation is derived to describe the traffic flow near the critical point. It is also shown that the modified Korteweg-de Veris (mKdV) equation is derived to describe the traffic jam. The connection between the TDGL and the mKdV equations is given.
引用
收藏
页码：1245 / 1250
页数：6
相关论文
共 23 条
[1]   DYNAMICAL MODEL OF TRAFFIC CONGESTION AND NUMERICAL-SIMULATION [J].
BANDO, M ;
HASEBE, K ;
NAKAYAMA, A ;
SHIBATA, A ;
SUGIYAMA, Y .
PHYSICAL REVIEW E, 1995, 51 (02) :1035-1042
[2]   Two velocity difference model for a car following theory [J].
Ge, H. X. ;
Cheng, R. J. ;
Li, Z. P. .
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2008, 387 (21) :5239-5245
[3]   Time-dependent Ginzburg-Landau equation for lattice hydrodynamic model describing pedestrian flow [J].
Ge Hong-Xia ;
Cheng Rong-Jun ;
Lo Siu-Ming .
CHINESE PHYSICS B, 2013, 22 (07)
[4]   Generalized force model of traffic dynamics [J].
Helbing, D ;
Tilch, B .
PHYSICAL REVIEW E, 1998, 58 (01) :133-138
[5]   Full velocity difference model for a car-following theory [J].
Jiang, R ;
Wu, QS ;
Zhu, ZJ .
PHYSICAL REVIEW E, 2001, 64 (01) :4-017101
[6]   Intermittent unstable structures induced by incessant constant disturbances in the full velocity difference car-following model [J].
Jiang, Rui ;
Wu, Qing-Song ;
Jia, Bin .
PHYSICA D-NONLINEAR PHENOMENA, 2008, 237 (04) :467-474
[7]   Lattice hydrodynamic traffic flow model with explicit drivers' physical delay [J].
Kang, Yi-Rong ;
Sun, Di-Hua .
NONLINEAR DYNAMICS, 2013, 71 (03) :531-537
[8]   CLUSTER EFFECT IN INITIALLY HOMOGENEOUS TRAFFIC FLOW [J].
KERNER, BS ;
KONHAUSER, P .
PHYSICAL REVIEW E, 1993, 48 (04) :R2335-R2338
[9]  
Li ZP, 2006, COMMUN THEOR PHYS, V46, P367
[10]   A lattice traffic model with consideration of preceding mixture traffic information [J].
Li Zhi-Peng ;
Liu Fu-Qiang ;
Sun Jian .
CHINESE PHYSICS B, 2011, 20 (08)
123