车辆跟驰模型的扭结-反扭结波解  

The Kink-Antikink Wave Solution of a Car-Following Model

作　　者：吴春秀[1] 陈明玉[1] WU Chunxiu;CHEN Mingyu(School of Mathematics and Computer Science>Quanzhou Normal University,Quanzhou Fujian 362000,China)

机构地区：[1]泉州师范学院数学与计算机科学学院,福建泉州362000

出　　处：《泉州师范学院学报》2021年第2期23-27,共5页Journal of Quanzhou Normal University

摘　　要：考虑前车和后车信息对当前车辆的影响,建立一个后视速度差车辆跟驰模型.运用渐近分析理论中的约化摄动方法,由该模型方程推导得出一个mKdV方程,讨论模型方程存在扭结-反扭结波解的必要条件,分析敏感率和后视权重对交通系统稳定性的影响,并通过数值模拟验证解析分析的结果.A backward looking velocity difference car-following model was proposed by considering the information of both the forward and backward cars. By using the reduction perturbation method of asymptotic analysis theory, a modified Korteweg-de Vries(mKdV) equation was derived from the car-following model and the necessary conditions for the existence of the kink-antikink solitary wave solution were discussed under a small perturbation. The influence of the sensitivity rate and the backward looking weight on the stability of traffic system was analyzed. The numerical results are consistent with the analytical ones.

关 键 词：车辆跟驰模型 约化摄动法 稳定性 扭结-反扭结波 

分 类 号：O29[理学—应用数学] U121[理学—数学]