Ge H X, Dai S Q, Xue Y, Dong L Y
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jun;71(6 Pt 2):066119. doi: 10.1103/PhysRevE.71.066119. Epub 2005 Jun 21.
Two lattice traffic models are proposed by incorporating a cooperative driving system. The lattice versions of the hydrodynamic model of traffic flow are described by the differential-difference equation and difference-difference equation, respectively. The stability conditions for the two models are obtained using the linear stability theory. The results show that considering more than one site ahead in vehicle motion leads to the stabilization of the system. The modified Korteweg-de Vries equation (the mKdV equation, for short) near the critical point is derived by using the reductive perturbation method to show the traffic jam which is proved to be described by kink-anti-kink soliton solutions obtained from the mKdV equations.
通过纳入协同驾驶系统，提出了两种格点交通模型。交通流流体动力学模型的格点版本分别由微分 - 差分方程和差分 - 差分方程描述。利用线性稳定性理论获得了这两种模型的稳定性条件。结果表明，在车辆运动中考虑前方多个位置会导致系统稳定。通过使用约化摄动方法，在临界点附近推导了修正的科特韦格 - 德弗里斯方程（简称为mKdV方程），以展示交通拥堵，事实证明交通拥堵可由从mKdV方程得到的扭结 - 反扭结孤子解来描述。
