Bifurcation analysis and control of a modified continuum traffic flow model considering mixed motor vehicles and bicycles

WenHuan Ai (), JianLi Fu (), JingMing Zeng () and DaWei Liu ()
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WenHuan Ai: Northwest Normal University
JianLi Fu: Northwest Normal University
JingMing Zeng: Northwest Normal University
DaWei Liu: Lanzhou Institute of Technology

The European Physical Journal B: Condensed Matter and Complex Systems, 2025, vol. 98, issue 4, 1-18

Abstract: Abstract In urban studies, issues with traffic flow have always been a popular topic. We explore the propagation traits and evolution law of traffic flow, which can serve as a theoretical foundation for the planning and management of road traffic, starting with the theory of traffic flow bifurcation. We suggest a macroscopic traffic model that takes into account the frictional and obstructive disturbance based on the influence of traffic flow mixed motor vehicles and bicycles. The influence of vehicle speed, density, speed differential, and other parameters on the evolution law of macroscopic traffic flow is investigated by bifurcation analysis. From the viewpoint of the overall stability of the traffic system, the non-linear bifurcation theory is also employed to describe the non-linear traffic phenomena on the traffic flow of mixed motor vehicles and bicycles. The findings indicate that when a blocking disturbance is certain, the unstable region of the traffic flow gradually expands as non-motorized traffic flow increases, and when a frictional disturbance is certain, the unstable region of the traffic flow gradually expands as the blocking disturbance's duration gradually lengthens. It has been discovered that the nonlinear model can accurately capture the phenomenon of mixed motor vehicles and bicycles in the traffic flow through the analysis of the equilibrium point and local bifurcation. Finally, this paper suggests a non-linear feedback controller that delays or prevents the emergence of bifurcation points when added to the model. This controller serves as a theoretical foundation for future research on the impact of mixed motor vehicles and bicycles on the operational characteristics of traffic flow. Through simulation of density-time and phase plane diagrams, the model is confirmed to be able to describe the phenomena of traffic congestion and stopping in real traffic, providing a theoretical foundation for the mitigation of traffic congestion. Graphical Abstract

Date: 2025
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DOI: 10.1140/epjb/s10051-025-00898-2

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