Ge, H.X., Meng, X.P., Zhu, K.Q. and Cheng, R.J. (2014) The Stability Analysis for an Extended Car Following Model Based on Control Theory. Chinese Physics Letters, 31, Article ID: 080505.
https://doi.org/10.1088/0256-307X/31/8/080505

has been cited by the following article:

• TITLE: Linear Stability and Nonlinear Analysis of an Extended Optimal Velocity Model Considering the Speed Limit

  AUTHORS: Guangzhu He, Cuncai Hua

  KEYWORDS: Optimal Velocity Model (OVM), Speed Limit, TDGL Equation, mKdV Equation

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.8 No.3, March 17, 2020

  ABSTRACT: In this paper, an extended car-following model is proposed based on an optimal velocity model (OVM), which takes the speed limit into consideration. The model is analyzed by using the linear stability theory and nonlinear analysis method. The linear stability condition shows that the speed limit can enlarge the stable region of traffic flow. By applying the reductive perturbation method, the time-dependent Ginzburg-Landau (TDGL) equation and the modified Korteweg-de Vries (mKdV) equation are derived to describe the traffic flow near the critical point. Furthermore, the relation between TDGL and mKdV equations is also given. It is clarified that the speed limit is essentially equivalent to the parameter adjusting of the driver’s sensitivity.