Bifurcation analysis of a speed gradient continuum traffic flow model

Wen-Huan Ai, Zhong-Ke Shi and Da-Wei Liu

Physica A: Statistical Mechanics and its Applications, 2015, vol. 437, issue C, 418-429

Abstract: A bifurcation analysis approach is presented based on the macroscopic traffic flow model. This method can be used to describe and predict the nonlinear traffic phenomena on the highway from a system global stability perspective. Based on a recently proposed speed gradient continuum traffic flow model, the types and stabilities of the equilibrium solutions are discussed and the existence of Hopf bifurcation and saddle–node bifurcation is proved. Then various bifurcations such as Hopf bifurcation, saddle–node bifurcation, Limit Point bifurcation of cycles, Cusp bifurcation and Bogdanov–Takens bifurcation are found and the traffic flow behaviors at some of them are analyzed. When the Hopf bifurcation is selected as the starting point of density temporal evolution, it may help to explain the stop-and-go traffic phenomena.

Keywords: Bifurcation analysis; Stability analysis; Nonlinear traffic phenomena; Stop-and-go (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:437:y:2015:i:c:p:418-429

DOI: 10.1016/j.physa.2015.06.004

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