Hopf bifurcation analysis and control of traffic flow model based on speed limit and lane change information of networked vehicles

Wenhuan Ai (), Yonghao Yang, Guoao Li and Xin Yang
Additional contact information
Wenhuan Ai: Northwest Normal University, College of Computer Science and Engineering
Yonghao Yang: Northwest Normal University, College of Computer Science and Engineering
Guoao Li: Northwest Normal University, College of Computer Science and Engineering
Xin Yang: Northwest Normal University, College of Computer Science and Engineering

The European Physical Journal B: Condensed Matter and Complex Systems, 2025, vol. 98, issue 12, 1-24

Abstract: Abstract 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. Graphical abstract

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1140/epjb/s10051-025-01084-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:eurphb:v:98:y:2025:i:12:d:10.1140_epjb_s10051-025-01084-0

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/10051

DOI: 10.1140/epjb/s10051-025-01084-0

Access Statistics for this article

The European Physical Journal B: Condensed Matter and Complex Systems is currently edited by P. Hänggi and Angel Rubio

More articles in The European Physical Journal B: Condensed Matter and Complex Systems from Springer, EDP Sciences
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().