Bifurcation analysis of a heterogeneous continuum traffic flow model

Abstract Motivated by the increasingly popular mixed traffic flow modeling, a novel heterogeneous continuum traffic flow model is proposed in this paper, which considers the differences of the driver's psychological headway and the driver's self-stabilizing effect on the optimal velocity related to the psychological headway. Leveraging the linear and nonlinear analysis approaches, the linear stability condition and the KdV-Burgers equation are yielded to describe the characteristic of traffic flow evolution. The bifurcation analysis on the proposed model is executed to discuss the existence and stability of Hopf bifurcation from a theoretical perspective. Numerical simulations are performed to verify the rationality of the abovementioned theory and explore the density evolution of heterogeneous traffic flow, including local cluster effect, fuel consumption and exhaust emissions and Hopf bifurcation, in which it is notable that the heterogeneous continuum traffic flow generates significantly different phenomena under different density conditions and the evolution of Hopf bifurcation in traffic flow is also involved.

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