分数阶多速度差模型的孤立波

Solitary waves of a fractional multispeed differential model

引入分数阶的多速度差模型,通过线性稳定性分析得到了模型的稳定性条件,结果显示分数阶模型的交通流稳定区域比整数阶模型扩大了.通过约化摄动法对模型分析获得了如下结果:在稳定流区域导出了描述密度波的Burgers方程,结果显示,三角激波随时间增加,且最终演化为均衡交通流;在不稳定区域的临界点附近导出修正的Korteweg-de Vries方程(简称为mKdV),由此得知扭结波的传播速度随着车辆数增加而变大,并且所获取的前车信息越多就越有利于交通拥堵的疏导;在亚稳态区域内,密度波则是按照KdV方程的孤立波变动的.

A fractional multi-velocity differential model is introduced.The stability condition of the model is obtained by the linear stability analysis.The result shows that the stability region of the traffic flow of the fractional order model is larger than that of the integer order model.By applying the reduced perturbation method to analyze the model,the following results are obtained:in the stability region,Burgers equation describing the density wave is derived.It shows that the triangle shock wave increases over time,and evolves into equilibrium traffic flow finally.In the unstable region near the critical point,the modified Korteweg-de Vries equation(mKdV for short)describing the density wave is derived.It shows that the propagation velocity of the kink wave becomes large as the number of vehicles increase.Meanwhile,the more information is acquired about the front vehicles,the more conduciveness is for the traffic jam;In the sub-stable region,the density wave varies according to the solitary wave of the KdV equation.