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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-de Vries(modified Korteweg-deVries,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-反扭结波解及KdV方程的孤波解描述了交通流堵塞现象.
By means of linear stability analysis, the stability conditions of multi-vehicle speed difference model are obtained, and it is found that the stability of traffic flow can be obviously enlarged by adjusting the information of many vehicles. The nonlinearity of this model is studied by means of reduced perturbation method Kinetic characteristics: In the steady flow regime, a Burgers equation describing the density wave is obtained. In the unstable region of the traffic flow, a modified Korteweg-de Vries (modified Korteweg-deVries, mKdV ) Equations are obtained; the KdV equation describing the headway distance is obtained near the neutral stability curve in the metastable region, the solitary wave solutions of Burgers, the kink-anti-kink solution of mKdV equation and the solitary wave solutions of KdV equation are described Flow blocked.