Nonlinear and bifurcation analysis for a novel heterogeneous continuum model and numerical tests

Abstract

In this paper, an improved heterogeneous continuum model is presented accounting for multiple optimal velocity functions with probabilities, in which self-stabilizing effect and velocity uncertainty are considered simultaneously. The linear stability criterion of this new model is obtained by applying linear stability theory. By means of nonlinear analysis method, the Korteweg-de Vries-Burgers (KdV-Burgers) equation is deduced to discuss the evolution process of traffic flow density wave. Through bifurcation analysis, the conditions and stability of the Hopf bifurcation for the new model are derived in detail. Numerical simulations are performed to study the influences of above mentioned factors on the stability of traffic flow. Fuel consumption and emissions are also explored in this paper. It is notable that when the Hopf bifurcation point is selected as the initial point of density evolution, significant periodic oscillations will occur in the traffic flow. The results of numerical simulations coincide well with the theoretical analysis.