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Analysis of Stability-To-Chaos in the Dynamic Evolution of Network Traffic Flows under a Dual Updating Mechanism

Author

Listed:
  • Shixu Liu

    (College of Civil Engineering, Fuzhou University, Fuzhou 350108, China)

  • Hao Yan

    (College of Civil Engineering, Fuzhou University, Fuzhou 350108, China)

  • Said M. Easa

    (Department of Civil Engineering, Ryerson University, Toronto, ON M5B 2K3, Canada)

  • Lidan Guo

    (College of Civil Engineering, Fuzhou University, Fuzhou 350108, China)

  • Yingnuo Tang

    (College of Civil Engineering, Fuzhou University, Fuzhou 350108, China)

Abstract

This paper proposes a traffic-flow evolutionary model under a dual updating mechanism that describes the day-to-day (DTD) dynamics of traffic flow and travel cost. To illustrate the concept, a simple two-route network is considered. Based on the nonlinear dynamic theory, the equilibrium stability condition of the system is derived and the condition for the division between the bifurcation and chaotic states of the system is determined. The characteristics of the DTD dynamic evolution of network traffic flow are investigated using numerical experiments. The results show that the system is absolutely stable when the sensitivity of travelers toward the route cost parameter ( θ ) is equal to or less than 0.923. The bifurcation appears in the system when θ is larger than 0.923. For values of θ equal to or larger than 4.402, the chaos appears in the evolution of the system. The results also show that with the appearance of chaos, the boundary and interior crises begin to appear in the system when θ is larger than 6.773 and 10.403, respectively. The evolution of network traffic flow is always stable when the proportion of travelers who do not change the route is 84% or greater.

Suggested Citation

  • Shixu Liu & Hao Yan & Said M. Easa & Lidan Guo & Yingnuo Tang, 2018. "Analysis of Stability-To-Chaos in the Dynamic Evolution of Network Traffic Flows under a Dual Updating Mechanism," Sustainability, MDPI, vol. 10(11), pages 1-17, November.
    • Handle: RePEc:gam:jsusta:v:10:y:2018:i:11:p:4182-:d:182556
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    References listed on IDEAS

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    2. Peng Niu & Yanming Sun & Zhuping Gong, 2021. "Research on the Chaotic Characteristics and Noise Reduction Prediction of Information System Anomalies in Equipment Manufacturing Enterprises," Sustainability, MDPI, vol. 13(9), pages 1-20, April.

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