Hartman-Grossman Hopf bifurcation control for traffic flow modelling of curves

Abstract

Bifurcation analysis of the stochastic behaviour of complex traffic flow systems can provide an in-depth understanding of the causes of various traffic phenomena, while bifurcation control on the basis of bifurcation analysis can effectively alleviate traffic congestion. In this paper, we firstly introduces an extended Aw-Rascle model considering the bend factor, and convert it into a traffic flow stability model suitable for bifurcation analysis. Then the macro traffic flow model of this curve is subjected to bifurcation analysis, and its stability conditions and the existence conditions of various types of bifurcations are derived, and the changes of trajectories near the equilibrium point and their corresponding traffic phenomena are described by the phase plane diagram. Finally, the bifurcation characteristics of the system are modified by the design of the feedback controller, such that the bifurcations appearing at the equilibrium point in the control system are shifted forward, backward, or disappeared, so that the effect of preventing or alleviating traffic congestion can be achieved. It is shown that the controlled system model can be adjusted by adjusting the values of the controller parameters to achieve the bifurcation point forward and backward, so that the unstable bifurcation point disappears, and to control the amplitude of the limit cycle formed by the Hopf bifurcation to control the stability of the system, and thus the bifurcation in the curved roadway traffic flow model provides a decision support for the traffic management.