Bifurcation Analysis and Control of Traffic Flow Model Considering the Impact of Smart Devices for Drivers

In order to comply with the development of intelligent transportation systems, many automotive suppliers upgrade motor vehicles, carrying a variety of intelligent vehicle equipment, which facilitates life but also has a lot of problems. Nowadays, intelligent devices have gradually become a new factor affecting traffic flow, but most traditional models rarely consider this factor and rarely use bifurcation theory methods to analyze traffic system state changes and control traffic flow state abrupt behavior. Without a full understanding of how smart devices affect traffic flow, the problem of traffic congestion cannot be solved well. In this paper, a macrotraffic flow model considering the influence of intelligent vehicle-borne communication devices is improved, which takes into account the change of drivers’ behavior under the influence of intelligent devices and thus the change of traffic flow state. A linear feedback controller is designed to analyze and control hopf bifurcation in the traffic flow system, so as to prevent or alleviate traffic congestion. First, a traffic flow stability model suitable for bifurcation analysis is established to transform the sudden change of traffic state into a system stability problem. The sudden change of stability, such as traffic congestion, is reflected from a macroperspective. Second, the bifurcation analysis of the traffic flow stability model is carried out to study the sudden change behavior of congestion and stability near the equilibrium point and bifurcation point of the expressway traffic system, and the change of actual traffic state is analyzed and predicted. Aiming at the unstable bifurcation points, a control scheme is designed by Chebyshev polynomial approximation and random feedback control to make the unstable bifurcation points delay or disappear and relieve traffic congestion. Finally, the simulation of hopf bifurcation control set on the model is carried out. The density space–time diagram and phase plane are used to verify the introduction of bifurcation control theory into traffic flow state control. It not only helps to improve the stability of traffic flow and avoid traffic jams but also provides a theoretical basis for the prevention of traffic jams. Numerical simulation results show that the improved model can well explain the formation and evolution mechanism of various congestion modes in real traffic, providing a scientific theoretical basis for preventing traffic congestion. And the addition of feedback controller to the model effectively inhibits traffic congestion, providing certain theoretical support for the implementation of effective traffic strategies and alleviating traffic congestion.