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Quantification of chaos in a time series generated from a traffic flow model using the extended entropic chaos degree

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  • Inoue, Kei
  • Tani, Kazuki

Abstract

Several Traffic flow models have been proposed to address the underlying causes of traffic congestion and develop effective methods for its suppression. Typically, these models are represented using differential or difference equations. Traffic flow models can exhibit chaotic behaviors. Traffic situations become unstable if chaos prevails in the traffic flow. Therefore, the conditions under which chaos occurs in the traffic flow and the intensity of chaos at that time must be investigated. The Lyapunov exponent is used for quantifying the chaos in the dynamical systems. However, computing the Lyapunov exponent over time series without a dynamical map is challenging. Recently, the extended entropic chaos degree has been introduced as an extension of the entropic chaos degree. The extended entropic chaos degree can be computed directly for any time series. Analytically, the extended entropic chaos degree equals the sum of all the Lyapunov exponents for multidimensional non-periodic maps. Moreover, the extended entropic chaos degree is mathematically shown to equal the sum of one positive and one negative Lyapunov exponents for two-dimensional typical chaotic maps, such as a generalized Baker’s map, and a standard map.

Suggested Citation

  • Inoue, Kei & Tani, Kazuki, 2023. "Quantification of chaos in a time series generated from a traffic flow model using the extended entropic chaos degree," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    • Handle: RePEc:eee:chsofr:v:176:y:2023:i:c:s0960077923010524
    DOI: 10.1016/j.chaos.2023.114150
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    References listed on IDEAS

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    1. Jian Gu & Shuyan Chen, 2014. "Nonlinear Analysis on Traffic Flow Based on Catastrophe and Chaos Theory," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-11, November.
    2. Nagatani, Takashi, 2005. "Chaos and dynamical transition of a single vehicle induced by traffic light and speedup," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 348(C), pages 561-571.
    3. Shang, Pengjian & Li, Xuewei & Kamae, Santi, 2005. "Chaotic analysis of traffic time series," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 121-128.
    4. Aderemi Adewumi & Jimmy Kagamba & Alex Alochukwu, 2016. "Application of Chaos Theory in the Prediction of Motorised Traffic Flows on Urban Networks," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-15, January.
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