Hopf bifurcation control of a modified continuum traffic flow model

Wenhuan Ai, Jianli Fu (), Na Li (), Dongliang Fang () and Dawei Liu ()
Additional contact information
Wenhuan Ai: College of Computer Science and Engineering, Northwest Normal University, Lanzhou, Gansu 730070, P. R. China†College of Electrical Engineering, Lanzhou Institute of Technology, Lanzhou, Gansu 730050, P. R. China
Jianli Fu: College of Computer Science and Engineering, Northwest Normal University, Lanzhou, Gansu 730070, P. R. China
Na Li: College of Computer Science and Engineering, Northwest Normal University, Lanzhou, Gansu 730070, P. R. China
Dongliang Fang: 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 09, 1-24

Abstract: The stability of the transportation system refers to the structural stability of the system. When the system structure is unstable, local or global bifurcation phenomena will occur, which is one of the main reasons for nonlinear traffic phenomena such as congestion. To truly understand the internal mechanism of the formation of these phenomena, it is necessary to analyze the bifurcation of traffic flow. In this paper, the Hopf bifurcation control of a modified viscous macroscopic traffic flow model is studied by using the linear state feedback method, which changes the characteristics of the bifurcation phenomenon of the dynamic system and obtains the required dynamic behavior of the system. First, we can convert the original traffic model into the nonlinear ordinary differential form suitable for bifurcation analysis, solve the equilibrium point of the system, and carry out phase plane analysis. Then, the linear state feedback term is added and the corresponding controlled system is generated, the existence and type of Hopf bifurcation and the existence of saddle node bifurcation are proved. Numerical simulation results show that the analysis and control of Hopf bifurcation in the traffic model are well realized in this paper.

Keywords: Traffic flow; equilibrium point; bifurcation analysis; Hopf bifurcation control (search for similar items in EconPapers)
Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0129183124501195
Access to full text is restricted to subscribers

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:wsi:ijmpcx:v:35:y:2024:i:09:n:s0129183124501195

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0129183124501195

Access Statistics for this article

International Journal of Modern Physics C (IJMPC) is currently edited by H. J. Herrmann

More articles in International Journal of Modern Physics C (IJMPC) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().