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Rich dynamics in some discrete-time car-following models

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  • Wang, Xiujuan
  • Peng, Mingshu

Abstract

There are a great number of works to study delay differential equations modeling road traffic, but fewer related to discrete-time car-following models. In this paper, we propose two classes of discrete-time car-following models, which can be viewed as leader–follower models or discretization version of classic continuous-time car-following models. Local stability analysis is established in details. Rich dynamical behavior is to be explored, including local stability analysis, chaotic behavior etc. Fractal properties are discovered by the computation of Lyapunov exponents and Lyapunov dimensions. High codimensional bifurcations can be expected. We find that one of the proposed models can admit infinite nontrivial fixed points in its equivalent form but the other cannot do. Moreover, if the leading vehicle presents a regular (steady states or periodic) or irregular (chaotic) oscillation pattern, the following is to do the same likely. In a sense, a synchronous/heredity property can be exhibited in the underlying model.

Suggested Citation

  • Wang, Xiujuan & Peng, Mingshu, 2019. "Rich dynamics in some discrete-time car-following models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    • Handle: RePEc:eee:phsmap:v:536:y:2019:i:c:s0378437119305540
    DOI: 10.1016/j.physa.2019.04.162
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    References listed on IDEAS

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    1. Denos C. Gazis & Robert Herman & Richard W. Rothery, 1961. "Nonlinear Follow-the-Leader Models of Traffic Flow," Operations Research, INFORMS, vol. 9(4), pages 545-567, August.
    2. Zhang, Xiaoyan & Jarrett, David F., 1997. "Stability analysis of the classical car-following model," Transportation Research Part B: Methodological, Elsevier, vol. 31(6), pages 441-462, November.
    3. Sun, Jie & Zheng, Zuduo & Sun, Jian, 2018. "Stability analysis methods and their applicability to car-following models in conventional and connected environments," Transportation Research Part B: Methodological, Elsevier, vol. 109(C), pages 212-237.
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    Citations

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    Cited by:

    1. Meng, Jingwei & Jin, Yanfei & Xu, Meng, 2023. "Stochastic dynamics of a discrete-time car-following model and its time-delayed feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 610(C).
    2. Cui, Bo-Yuan & Zhang, Geng & Ma, Qing-Lu, 2021. "A stable velocity control strategy for a discrete-time car-following model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 571(C).
    3. Liu, Bo & Zhang, Geng, 2021. "A double velocity control method for a discrete-time cooperative driving system with varying time-delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).

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