Bifurcation analysis for a novel heterogeneous continuum model considering electronic throttle angle changes with memory

Heterogeneous traffic flow model such as mixes of trucks and cars or connected and regular vehicles is a central issue in traffic flow modeling. However, few researches focus on the bifurcation phenomena of heterogeneous traffic flow. Due to this point, a novel heterogeneous continuum model accounting for different ratios of multiple optimal velocity functions is proposed, in which electronic throttle angle changes with memory is also considered. A simple formula for the linear stability criterion of this improved model is theoretically deduced, and the Korteweg-de Vries-Burgers (KdV-Burgers) equation is derived to discuss the characteristics of density evolution through nonlinear analysis method. The conditions and stability of the Hopf bifurcation for the modified model are then proved minutely. Numerical simulations are executed to investigate how multiple maximum velocities, multiple safety spacings and electronic throttle angle changes with memory affect the density fluctuations, in which numerical experiments on fuel consumptions and emissions are also included. To address the problems mentioned above, we set the Hopf bifurcation as the initial point of the heterogeneous continuum traffic flow to analyze the evolution of bifurcation behavior in the heterogeneous traffic flow.