Bifurcation control and analysis of traffic flow model based on driver prediction effect

Based on the measured data, in this paper, we find that there are significant differences in the ideal speed of drivers with different attributes during their driving process. Through wavelet analysis, it is proved that the regularity of the car-following behavior of the driver is poor in a short time, and it cannot be predicted and analyzed at a small time scale. As one of the important participants in the traffic system, it is necessary to consider the driving behavior factors in the traffic flow model. Therefore, in this paper, we propose a nonuniform continuous traffic flow model. Based on the difference in the expected headway of the driver, the model considers the self-stabilization effect of the prediction time of the driver on the optimal speed difference and considers control theory to further improve the model. Through this model, the bifurcation theory can be applied to the stability analysis of the traffic system to study the stability mutation behavior of the traffic system at the bifurcation point. Through linear and nonlinear analysis methods, the stability conditions of the model can be derived, and the type of equilibrium point of the model can be judged. In addition, the random function is applied to the traffic model, and the bifurcation control is carried out for the bifurcation behavior in the traffic; that is, the bifurcation characteristics of the traffic system are changed by designing linear and nonlinear random feedback controllers. In this paper, we theoretically prove the existence conditions and types of Hopf bifurcation at the equilibrium point of the model and analyze the internal causes of the stability mutation of the traffic flow through the Hopf bifurcation point. Then a feedback controller is designed to control the amplitude of the Hopf bifurcation and the limit cycle formed by the Hopf bifurcation. Finally, the theoretical derivation results are verified by experimental numerical simulation. In this paper, we show that, by adjusting the control parameters of the feedback controller, the Hopf bifurcation of the stochastic system can be delayed or even eliminated, and the amplitude of the limit cycle formed by the Hopf bifurcation can be adjusted to achieve the purpose of controlling the stability of the traffic system and prevent or alleviate traffic congestion.