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Wang, P., Yu, G., Wu, X. and Wang, Y. (2017) Linear and Nonlinear Stability Analysis of an Extended Car-Following Model Considering Pedestrians on Adjacent Lane. Nonlinear Dynamics, 88, 777-789.
https://doi.org/10.1007/s11071-016-3275-2

has been cited by the following article:

• TITLE: Criterion for the Emergence of Meta-Stable States in Traffic Systems

  AUTHORS: Liuhua Zhu

  KEYWORDS: Traffic Flow, Cellular Automaton, Matthew Effect, Hysteresis Loop Meta-Stable State

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.8 No.6, June 1, 2020

  ABSTRACT: The measurements on actual traffic have revealed the existence of meta-stable states with high flow. Such nonlinear phenomena have not been observed in the classic Nagel-Schreckenberg traffic flow model. Here we just add a constraint to the classic model by introducing a velocity-dependent randomization. Two typical randomization strategies are adopted in this paper. It is shown that the Matthew effect is a necessary condition to induce traffic meta-stable states, thus shedding a light on the prerequisites for the emergence of hysteresis loop in the fundamental diagrams.