https://doi.org/10.1140/epjb/s10051-025-01084-0
Research - Statistical and Nonlinear Physics
Hopf bifurcation analysis and control of traffic flow model based on speed limit and lane change information of networked vehicles
College of Computer Science and Engineering, Northwest Normal University, 730070, Lanzhou, Gansu, China
Received:
29
May
2025
Accepted:
29
October
2025
Published online:
2
December
2025
Building upon the integration of bifurcation theory from nonlinear dynamics and traffic flow theory, this paper incorporated road speed limit information and lane change behavior provided by intelligent vehicle networks during the driving process. A macroscopic traffic flow model was proposed to address critical challenges in traffic system stability analysis, sudden behavioral transitions, and feedback control design. The equilibrium solutions of the proposed model – considering both speed limits and lane change information – were analyzed using differential equation theory. The dynamic behavior near these equilibrium points was visualized through phase plane diagrams, providing a foundation for subsequent theoretical investigations. Based on this analysis, the existence conditions and types of Hopf bifurcations were derived theoretically, describing how traffic congestion and system stability evolve under varying conditions. The critical point of system mutation was identified and analyzed to explore the mechanism behind global stability changes, providing technical support for preventing and mitigating traffic congestion. Focusing on the unstable dynamics near bifurcation points, a stochastic function was introduced into an improved Full Velocity Difference Model (FVDM) to examine how bifurcation behaviors manifest in traffic flow. A control mechanism was designed to stabilize the system by adjusting its parameters, thereby modifying the existence and amplitude of Hopf bifurcations. This approach effectively suppresses unstable oscillatory behavior, reduces periodic fluctuations in traffic density, and enhances overall traffic flow stability. Finally, simulations involving spatio-temporal density diagrams, phase plane plots, and real-world public traffic datasets were conducted to validate the influence of speed limit and lane change information on driver decision-making. The impact of the feedback controller on system stability was also demonstrated, thereby enabling the optimization of traffic control strategies. The findings contribute to intelligent transportation planning and support future developments in autonomous driving and connected vehicle systems.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
