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多前车速度差的车辆跟驰模型的稳定性与孤波
Analysis of the stability and solitary waves for multi-velocity difference car-following model of traffic flow
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摘要: 通过线性稳定性分析，得到了多前车速度差模型的稳定性条件，并发现通过调节多前车信息，使交通流的稳定区域明显扩大．通过约化摄动方法研究了该模型的非线性动力学特性：在稳定流区域，得到了描述密度波的Burgers方程；在交通流的不稳定区域内，在临界点附近获得了描述车头间距的修正的Korteweg—deVries（modified Korteweg-de Vries，mKdV）方程；在亚稳态区域内，在中性稳定曲线附近获得了描述车头间距的KdV方程．Burgers的孤波解、mKdV方程的扭结一反扭结波解及KdV方程的孤波解描述了交通流堵塞现象．Abstract: This article deals with the characteristic of the multiple velocity difference car-following model. We obtain the stability conditions of the model by using the linear stability analysis, and find that the stable region is apparently enlarged by adjusting the information about the multi-velocity difference. We study the nonlinear characteristics of the model by applying the reductive perturbation method. We obtain the Burgers equation and the modified Korteweg-de-Vries （mKdV） equation around the critical point and the Korteweg-de- Vries （KdV） equation near the neutral stability line in the stable region and the unstable region and the metastable region. The soliton solution of Burgers equation, the kink-antikink solution of mKdV equation, and the solition solution of KdV equation describe the traffic jams.
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