KdV–Burgers equation in the modified continuum model considering anticipation effect

2015 ◽  
Vol 438 ◽  
pp. 26-31 ◽  
Author(s):  
Huaqing Liu ◽  
Pengjun Zheng ◽  
Keqiang Zhu ◽  
Hongxia Ge
Keyword(s):  
Continuum Model ◽  
Burgers Equation ◽  
Anticipation Effect

Solition Wave of Car-Following Model with Anticipation Effect

2015 ◽  
Vol 738-739 ◽  
pp. 504-507
Author(s):  
Ji Qun Wu ◽  
Shuang Ke Li
Keyword(s):  
Burgers Equation ◽  
Kdv Equation ◽  
Mkdv Equation ◽  
Reductive Perturbation Method ◽  
Nonlinear Characteristics ◽  
Car Following ◽  
De Vries ◽  
Car Following Model ◽  
Anticipation Effect ◽  
Solition Wave

In this paper, the nonlinear analysis is conducted for the car-following model with the consideration of the anticipation effect in single line, which was proposed by Peng guanghan. We study the nonlinear characteristics of the model by applying the reductive perturbation method, and drive the Burgers equation, the Korteweg-de-Vries (KDV) equation and the modified Korteweg-de-Vries (MKDV) equation respectively. We find that the above nonlinear equations for this model are identical with those equations for the Full velocity difference model.

KdV-Burgers equation in the modified continuum model considering the “backward looking” effect

2017 ◽  
Vol 91 (3) ◽  
pp. 2007-2017 ◽  
Author(s):  
Zhaoze Liu ◽  
Jufeng Wang ◽  
Hongxia Ge ◽  
Rongjun Cheng
Keyword(s):  
Continuum Model ◽  
Burgers Equation

The KdV–Burgers equation in a new continuum model with consideration of driverʼs forecast effect and numerical tests

2013 ◽  
Vol 377 (44) ◽  
pp. 3193-3198 ◽  
Author(s):  
Hong-Xia Ge ◽  
Ling-Ling Lai ◽  
Peng-Jun Zheng ◽  
Rong-Jun Cheng
Keyword(s):  
Continuum Model ◽  
Burgers Equation ◽  
Numerical Tests

scholarly journals The Burgers Equation for a New Continuum Model with Consideration of Driver’s Forecast Effect

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Lei Yu ◽  
Bingchang Zhou
Keyword(s):  
Continuum Model ◽  
Burgers Equation ◽  
Density Wave ◽  
Reductive Perturbation Method ◽  
Stable Region ◽  
Local Cluster ◽  
New Model ◽  
Stop And Go ◽  
The Stability ◽  
Positive Effect

A new continuum model with consideration of driver’s forecast effect is obtained to study the density wave problem and the stop-and-go phenomena. The stability condition of the new model is derived by using linear analysis. The triangular shock wave, one type of density wave, which is determined by Burgers equation in the stable region, is discussed in great detail with reductive perturbation method. The local cluster appears when we perform the numerical simulations for the new model. It also proves that the driver’s forecast effect has the positive effect of reducing the local cluster.

Macro autonomous traffic flow model with traffic jerk and downstream vehicle information

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Zhai Cong ◽  
Weitiao Wu
Keyword(s):  
Traffic Congestion ◽  
Continuum Model ◽  
Burgers Equation ◽  
Positive Impact ◽  
Opening Angle ◽  
Nonlinear Stability Analysis ◽  
Content Type ◽  
Traffic Jam ◽  
Traffic Jerk ◽  
The Stability

PurposeTo reflect the future traffic environment, the authors simultaneously incorporate the electronic throttle (ET) and traffic jerk into the traditional continuum model. The authors derive the stability criterion of the enhanced continuum model via the perturbation method.Design/methodology/approachTo facilitate insight into the propagation and evolution mechanism of traffic jam near the stability condition, the authors use the nonlinear stability analysis method to derive the KdV-Burgers equation of proposed continuum model. Finally, the numerical example verified that the new item of ET opening angle and traffic jerk have a positive impact on suppressing traffic congestion and improving road robustness.FindingsThe new item of ET opening angle and traffic jerk have a positive impact on suppressing traffic congestion and improving road robustness.Originality/valueTo better reflect the real traffic environment, a extend continuum model taking into account the ET opening angle and traffic jerk effect is presented. The stability criterion of the extended model is got based on perturbation method. The evolution characteristics and propagation mechanism of the traffic jam near the neutral stability condition are further received by deriving the KdV-Burgers equation in the nonlinear stability analysis. From simulation, we found that the ET opening angle information and traffic jerk have a significant effect on the traffic jam.

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