Bifurcation analysis of macroscopic traffic flow models based on driver behavior

WenHuan Ai, YiFan Zhang (), DanDan Xing () and DaWei Liu ()
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WenHuan Ai: College of Computer Science and Engineering, Northwest Normal University, Lanzhou, Gansu 730070, P. R. China
YiFan Zhang: College of Computer Science and Engineering, Northwest Normal University, Lanzhou, Gansu 730070, P. R. China
DanDan Xing: College of Computer Science and Engineering, Northwest Normal University, Lanzhou, Gansu 730070, P. R. China
DaWei Liu: ��College of Electrical Engineering, Lanzhou Institute of Technology, Lanzhou, Gansu 730050, P. R. China

International Journal of Modern Physics C (IJMPC), 2024, vol. 35, issue 08, 1-38

Abstract: This paper proposes a novel nonuniform continuous traffic flow model, which takes into account the differences in drivers’ expected headway and further improves the model by incorporating the influences of relative distance and relative velocity of vehicles through linear weighting. Additionally, the model also considers the dynamic response time of drivers for further refinement. With this model, bifurcation theory can also be applied in the stability analysis of traffic systems to study the stability mutation behavior of traffic systems at bifurcation points. Through linear and nonlinear analysis methods, the stability conditions of the model and the KdV–Burgers equation can be derived, the type of equilibrium point of the model can be judged, the conditions for the existence of Hopf bifurcations and the type of bifurcations can be proved, and the traffic flow problem can be transformed into the stability analysis problem of the system. Through numerical simulations in both high-density and low-density scenarios, it is shown that the model can well describe the actual traffic phenomena and can describe the stability abrupt behavior of the traffic system at Hopf bifurcation points and saddle-node bifurcation points through density-time and phase plane diagrams.

Keywords: Bifurcation analysis; stability analysis; traffic flow; driver behavior (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0129183124500931

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