Bifurcation analysis of an extended macro model considering time delay and anticipation effect

In this paper, a novel macro traffic flow model is proposed integrating time delay and anticipation effect on the headway and velocity, which are indispensable factors in the course of driving. The stability condition of the novel model is derived by linear stability analysis method. The corresponding stability diagrams show that time delay deteriorates the stability of traffic flow, while anticipation effect is conducive to traffic flow stability. The existence and stability of Hopf bifurcations are discussed through bifurcation theory. Numerical results demonstrate that the improved continuum model presented can well describe the local cluster effect, fuel consumption and exhaust emissions. Considering the factor of anticipation and time delay has positive and negative impact on dynamic characteristic of macroscopic flow, respectively. In Hopf bifurcation simulation, partial data from Portable Emissions Measurement System (PeMS) is adopted to calibrate the parameters of the novel model. Meanwhile, the simulation results verify the existence of Hopf bifurcation. The occurrence of bifurcations brings a significant impact on the stability of traffic flow, in which the density wave of traffic flow arises equal-amplitude oscillations. (C) 2021 Elsevier B.V. All rights reserved.