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Hopf bifurcation control of macroscopic traffic flow model considering vehicle braking effect

  • Regular Article - Flowing Matter
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Abstract

Traffic congestion not only has a great impact on people's travel, but also increases energy consumption and air pollution. The control analysis of the macroscopic traffic flow model considering the vehicle braking effect is particularly important, reflecting the impact on the actual traffic flow density wave, so as to better solve the actual traffic problems. In this paper, based on a speed difference optimization speed model, the micro–macro-variables are transformed into a high-order continuous traffic flow model. Then, a random function considering the physical correlation of random components is added to the high-order continuous traffic flow model to establish a random traffic flow model that can reflect the uncertain behavior of traffic flow acceleration or deceleration. Based on this stochastic traffic model, the existence of Hopf bifurcation and bifurcation control of the traffic flow system model considering stochastic characteristics are derived by using Hopf bifurcation theorem. By Chebyshev polynomial approximation method, the stochastic problem of the system is transformed into the bifurcation control problem of its equivalent deterministic system. A feedback controller is designed to delay the occurrence of Hopf bifurcation and control the amplitude of the limit cycle. Without changing the equilibrium point of the system, the complete elimination of Hopf bifurcation can be achieved by controlling the amplitude of the limit cycle. That is, the feedback controller is used to modify the bifurcation characteristics of the system, such as the bifurcation appearing at the equilibrium point in the control system moves forward, moves backward or disappears, so as to achieve the effect of preventing or alleviating traffic congestion.

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Data availability

1. The research model comes from reference [30]. 2. The data used to support the findings of this study are included within the article. 3. Simulation data, codes and so on can be obtained from the second author during the period of research. We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled. The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

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Authors and Affiliations

  1. College of Computer Science and Engineering, Northwest Normal University, Lanzhou, 730070, Gansu, China

    WenHuan Ai & MingMing Wang

  2. College of Electrical Engineering, Lanzhou Institute of Technology, Lanzhou, 730050, Gansu, China

    DaWei Liu

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  1. WenHuan Ai
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  2. MingMing Wang
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Contributions

WA participated in the research, proposed research topics, designed the research scheme, implemented the research process and contributed to the final paper. MW contributed to the article writing, performed the research, collated the literature, designed the paper framework, drafted the paper, revised the thesis and organized the data. DL supported the work, performed the statistical analysis, contributed to the access to research funding, technical or material support and instructional support.

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Correspondence to WenHuan Ai.

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Ai, W., Wang, M. & Liu, D. Hopf bifurcation control of macroscopic traffic flow model considering vehicle braking effect. Eur. Phys. J. E 46, 130 (2023). https://doi.org/10.1140/epje/s10189-023-00393-5

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