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Hopf bifurcation control of a modified continuum traffic flow model

Author

Listed:
  • 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)

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.

Suggested Citation

  • Wenhuan Ai & Jianli Fu & Na Li & Dongliang Fang & Dawei Liu, 2024. "Hopf bifurcation control of a modified continuum traffic flow model," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 35(09), pages 1-24, September.
    • Handle: RePEc:wsi:ijmpcx:v:35:y:2024:i:09:n:s0129183124501195
    DOI: 10.1142/S0129183124501195
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