Bifurcation analysis based on new macro two-velocity difference model

Author:

Ai Wenhuan1ORCID,Ma Yunfei1,Liu Dawei2

Affiliation:

1. Department of Computer Science & Engineering, Northwest Normal University, Lanzhou, Gansu, P. R. China

2. College of Electrical Engineering, Lanzhou Institute of Technology, Lanzhou, Gansu 730050, P. R. China

Abstract

Based on the new macroscopic two-velocity difference model, this paper analyzes the linear stability of the new model and studies the nonlinear bifurcation theory. First, the linear stability analysis method is used to study the stability conditions of the shock wave in the model. Then, considering the long wave model in the coarse-grained scale, the reduced perturbation method is used to analyze the characteristics of the traffic flow in the metastable region, and the solitary wave solution of the Korteweg-de Vries (KdV) equation in the metastable region is derived. In addition, by using the bifurcation analysis method, the type, and stability of the equilibrium solution are discussed and the existing conditions of the saddle-node bifurcation are proven. Then, taking the saddle-node bifurcation as the starting point, we draw the density space-time diagram and phase plane diagram of the system. It is proven that the newly proposed model can describe complex traffic phenomena such as stop-and-go and sudden changes in stability, which is of great help to solve traffic congestion.

Funder

National Natural Science Foundation of China

Natural Science Foundation of Gansu Province of China

China Postdoctoral Science Foundation Funded Project

Qizhi Personnel Training Support Project of Lanzhou Institute of Technology

Gansu University Innovation Fund Project

Publisher

World Scientific Pub Co Pte Ltd

Subject

Physics and Astronomy (miscellaneous)

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3