https://doi.org/10.1140/epjb/s10051-022-00469-9
Regular Article - Statistical and Nonlinear Physics
Two-parameter bifurcation and energy consumption analysis of the macro traffic flow model
1
School of Science, North China University of Technology, 5 Jinyuanzhuang Road, 100144, Bejing, China
2
School of Electrical and Control Engineering, North China University of Technology, 5 Jinyuanzhuang Road, 100144, Bejing, China
3
School of Automation, Beijing Institude of Technology, 5 Zhongguancun South Street, 100081, Bejing, China
Received:
20
September
2022
Accepted:
12
December
2022
Published online:
28
December
2022
Bifurcation of traffic flow involves complex dynamic characteristics of the system. In order to understand the complex traffic phenomenon, this work designed a macro traffic model considering the driver’s memory which plays an important role in the traffic flow. Based on this model, we investigate the effects of the driver’s memory and wave velocity on the stability of the traffic flow. By means of one and two parameter bifurcation analysis, we explore how these parameters affect the bifurcation structure of the system, and further investigate the dynamic mechanisms of traffic flow. We explain various traffic phenomena related to the different types of equilibrium points and limit cycles by phase plane analysis. We also study how the initial density and bifurcation structure affect the energy consumption in the system. The results show that the driver’s memory and wave velocity play an important role in the stability of the traffic flow. By considering the change of bifurcation structure, we can better understand the source of traffic congestion, and further predict and control the possible traffic congestion.
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