Bifurcation analysis of traffic flow through an improved car-following model considering the time-delayed velocity difference

Abstract

In this paper a new car-following model with consideration of time-delayed velocity difference is proposed to investigate the effect of time-delayed velocity on traffic flow via bifurcation analysis. Based on this model, the linear stability analysis is carried out and the corresponding stability condition is obtained. Then the Hopf bifurcation analysis is performed in term of theoretical analysis and numerical simulation. The result shows that there exist Hopf bifurcation critical points and the position of the critical points is found to be located on the boundary of the instability region. Finally, the influence of the delay time and sensitivity of velocity difference on Hopf bifurcation is discussed, respectively.