{"title":"Bifurcation Analysis of the Macroscopic Traffic Flow Model Based on Driver’s Anticipation and Traffic Jerk Effect","authors":"W. H. Ai, L. Xu, T. Zhang, D. W. Liu","doi":"10.1134/s0015462823601249","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Based on realistic traffic conditions, the macroscopic traffic flow model that considers the driver’s anticipation and traffic jerk effect is improved, and the bifurcation theory is used to describe and predict nonlinear traffic phenomena on the road from the perspective of global stability. Firstly, the linear stability conditions and the Korteweg–de Vries–Burgers equation are derived using linear and nonlinear methods to characterize the evolution of traffic flow. The type and stability of the equilibrium solution are discussed using the bifurcation analysis method, and the conditions of existence of the Hopf bifurcation and saddle-node bifurcation are proved. Numerical simulations show that the model can describe the complex nonlinear dynamic phenomena observed on the road. The bifurcation analysis will be helpful for improving our understanding of stop-and-go and sudden changes in stability in real traffic flow.</p>","PeriodicalId":560,"journal":{"name":"Fluid Dynamics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fluid Dynamics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1134/s0015462823601249","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
Based on realistic traffic conditions, the macroscopic traffic flow model that considers the driver’s anticipation and traffic jerk effect is improved, and the bifurcation theory is used to describe and predict nonlinear traffic phenomena on the road from the perspective of global stability. Firstly, the linear stability conditions and the Korteweg–de Vries–Burgers equation are derived using linear and nonlinear methods to characterize the evolution of traffic flow. The type and stability of the equilibrium solution are discussed using the bifurcation analysis method, and the conditions of existence of the Hopf bifurcation and saddle-node bifurcation are proved. Numerical simulations show that the model can describe the complex nonlinear dynamic phenomena observed on the road. The bifurcation analysis will be helpful for improving our understanding of stop-and-go and sudden changes in stability in real traffic flow.
期刊介绍：
Fluid Dynamics is an international peer reviewed journal that publishes theoretical, computational, and experimental research on aeromechanics, hydrodynamics, plasma dynamics, underground hydrodynamics, and biomechanics of continuous media. Special attention is given to new trends developing at the leading edge of science, such as theory and application of multi-phase flows, chemically reactive flows, liquid and gas flows in electromagnetic fields, new hydrodynamical methods of increasing oil output, new approaches to the description of turbulent flows, etc.
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