考虑限速的最优速度模型的稳定性与孤波
The Stability and Soliton of the Optimal Velocity Model Considering Speed Limit
DOI: 10.12677/IJM.2019.83021, PDF,    国家自然科学基金支持
作者: 和光珠, 化存才*：云南师范大学数学学院，云南 昆明
关键词: 最优速度模型；限速；稳定性；密度波；The Optimal Velocity Model； Speed Limit； Stability； Density Wave
摘要: 本文基于最优速度模型，设计了考虑驾驶员提前时间获知限速信息的交通流模型。利用线性稳定性分析方法，得到了模型的稳定性条件。表明限速信息的影响使得交通流的稳定区域有明显扩大。利用约化摄动法对模型进行分析，分别在稳定区域、亚稳态区域和不稳定区域导出密度波方程——Burgers方程、KdV方程和mKdV方程。通过Burgers方程、KdV方程的孤波解以及mKdV方程的扭结–反扭结波解描述了提前获知限速信息下的交通流堵塞现象。
Abstract: Based on the optimal velocity model, this paper designs a traffic flow model which takes into ac-count the driver’s advance time to know the speed limit information. By using the linear stability analysis method, the stability condition of the model is obtained. It shows that the influence of the speed limit makes the stable region of traffic flow expand obviously. The density wave equations such as Burgers equation, KdV equation and mKdV equation are derived respectively from the reduced perturbation method in the stable region, metastable region and unstable region. The phenomena of traffic congestion under the speed limit are described by the solitary wave solution of Burgers and KdV equation, and by the kink-antikink solution of mKdV equation.
文章引用：和光珠, 化存才. 考虑限速的最优速度模型的稳定性与孤波[J]. 力学研究, 2019, 8(3): 187-196. https://doi.org/10.12677/IJM.2019.83021

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