Analytical solutions of pattern formation for a class of discrete Aw–Rascle–Zhang traffic models

Yuri B. Gaididei, Peter L. Christiansen, Mads Peter Sørensen*, Jens Juul Rasmussen

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

A follow-the-leader model of traffic flow is considered in the framework of the discrete Aw–Rascle–Zhang model which is a combination of the nonlinear General Motors model and the Optimal Velocity model. In this model, which is studied on a closed loop, stable and unstable pulse or jam patterns emerge. Analytical investigations using truncated Fourier analysis show that the appearance of the jam patterns is due to supercritical Hopf bifurcations. These results are confirmed and supplemented by numerical simulations. In addition, a link between the discrete Aw–Rascle–Zhang model and the modified Optimal Velocity model is established.

Original languageEnglish
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume73
Pages (from-to)391-402
Number of pages12
ISSN1007-5704
DOIs
Publication statusPublished - 2019

Keywords

  • Complex systems
  • Interdisciplinary applications of physics
  • Ordinary differential equations
  • Pattern formation
  • Traffic modeling

Cite this

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title = "Analytical solutions of pattern formation for a class of discrete Aw–Rascle–Zhang traffic models",
abstract = "A follow-the-leader model of traffic flow is considered in the framework of the discrete Aw–Rascle–Zhang model which is a combination of the nonlinear General Motors model and the Optimal Velocity model. In this model, which is studied on a closed loop, stable and unstable pulse or jam patterns emerge. Analytical investigations using truncated Fourier analysis show that the appearance of the jam patterns is due to supercritical Hopf bifurcations. These results are confirmed and supplemented by numerical simulations. In addition, a link between the discrete Aw–Rascle–Zhang model and the modified Optimal Velocity model is established.",
keywords = "Complex systems, Interdisciplinary applications of physics, Ordinary differential equations, Pattern formation, Traffic modeling",
author = "Gaididei, {Yuri B.} and Christiansen, {Peter L.} and S{\o}rensen, {Mads Peter} and Rasmussen, {Jens Juul}",
year = "2019",
doi = "10.1016/j.cnsns.2019.02.026",
language = "English",
volume = "73",
pages = "391--402",
journal = "Communications in Nonlinear Science and Numerical Simulation",
issn = "1007-5704",
publisher = "Elsevier",

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TY - JOUR

T1 - Analytical solutions of pattern formation for a class of discrete Aw–Rascle–Zhang traffic models

AU - Gaididei, Yuri B.

AU - Christiansen, Peter L.

AU - Sørensen, Mads Peter

AU - Rasmussen, Jens Juul

PY - 2019

Y1 - 2019

N2 - A follow-the-leader model of traffic flow is considered in the framework of the discrete Aw–Rascle–Zhang model which is a combination of the nonlinear General Motors model and the Optimal Velocity model. In this model, which is studied on a closed loop, stable and unstable pulse or jam patterns emerge. Analytical investigations using truncated Fourier analysis show that the appearance of the jam patterns is due to supercritical Hopf bifurcations. These results are confirmed and supplemented by numerical simulations. In addition, a link between the discrete Aw–Rascle–Zhang model and the modified Optimal Velocity model is established.

AB - A follow-the-leader model of traffic flow is considered in the framework of the discrete Aw–Rascle–Zhang model which is a combination of the nonlinear General Motors model and the Optimal Velocity model. In this model, which is studied on a closed loop, stable and unstable pulse or jam patterns emerge. Analytical investigations using truncated Fourier analysis show that the appearance of the jam patterns is due to supercritical Hopf bifurcations. These results are confirmed and supplemented by numerical simulations. In addition, a link between the discrete Aw–Rascle–Zhang model and the modified Optimal Velocity model is established.

KW - Complex systems

KW - Interdisciplinary applications of physics

KW - Ordinary differential equations

KW - Pattern formation

KW - Traffic modeling

U2 - 10.1016/j.cnsns.2019.02.026

DO - 10.1016/j.cnsns.2019.02.026

M3 - Journal article

VL - 73

SP - 391

EP - 402

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

SN - 1007-5704

ER -