Bifurcation Phenomenon Analysis Of Traffic Flow Based On Driver’s Behavior Model

With the rapid development of social economy and technology,as well as the improvement of people’s requirement for travel quality,the development of transportation construction is also getting faster and faster.Traffic congestion has become a common problem hindering urban development,solving this problem requires in-depth research on traffic phenomena.The detailed description of traffic system is an important guarantee for studying the evolution of vehicle behavior in traffic flow and is the basis for the study of traffic system.Macroscopic traffic flow modeling is generally devoted to studying the global evolution process of traffic flow state,laying a theoretical foundation for better exploring actual traffic flow.As the core of the driving process,driver’s behavior has a certain impact on traffic flow.Therefore,starting from the actual situation,the bifurcation phenomenon of traffic flow based on a macro road traffic model of driver’s behavior is studied in this paper.One of the main problems is how to fundamentally alleviate and control traffic congestion by analyzing the characteristics and the change of traffic flow state,investigating the inherent mechanism of traffic congestion.In this paper,the problem of traffic flow is linked to the stability of the system,the nonlinear characteristics and state changes of traffic flow phenomena are mainly studied by using phase plane analysis and bifurcation theory.The main work of this article is as follows:(1)A macroscopic traffic flow model considering driver’s reaction time and distance is improved to address the factor of driver’s reaction delay and stability analysis is conducted.Firstly,the linear stability condition and the density waves in the metastable region of the model are analyzed by using the small perturbation method and the reductive perturbation method,respectively.Then,the traffic flow model is transformed into a model suitable for phase plane analysis through traveling wave substitution,and the traffic flow problem is transformed into the stability analysis problem of the model,the type and stability of the equilibrium point is analyzed.Finally,phase plane diagrams are drawn to analyze the distribution of the trajectory near the equilibrium point and the global structure of the phase plane diagram,and the evolution of uniform traffic flow adding a small perturbation is simulated and analyzed by using the finite difference method.The results show that the model can describe nonlinear local cluster phenomena observed in traffic system.Analyzing the stability of traffic flow system and other nonlinear kinematic characteristics through phase plane not only helps to better describe the nonlinear dynamic phenomena of traffic flow,but also provides support for the research of common state mutation phenomena in traffic flow.(2)A corresponding driver’s forecast viscous macro traffic model is established based on a car-following model considering driver’s forecast behavior and bifurcation analysis of traffic flow is conducted.Firstly,the linear stability analysis of the new model shows that adding driver’s forecast term can improve the stability of traffic flow.Then,the bifurcation theory is applied to the traffic flow model to study the nonlinear dynamic bifurcation behavior in the traffic flow from the equilibrium point,analyze the phenomenon of sudden change of traffic flow state,the existence conditions of Hopf bifurcation and saddle-node bifurcation and the type of Hopf bifurcation are derived theoretically.Finally,various bifurcation points of the model are obtained through simulation,and through phase plane and density space-time diagrams,the abrupt state change of traffic flow when variable parameter pass through these bifurcation points are analyzed from different perspectives,revealing the internal mechanism of instability phenomena such as stop-and-go behavior in the traffic system,and thus describing and predicting traffic phenomena from the perspective of system stability.(3)On the basis of bifurcation analysis of the driver’s forecast macro traffic model,Hopf bifurcation control of traffic flow is studied.Various control strategies are specified for unstable bifurcation points to make them stable or disappear in order to achieve an ideal traffic state.In this paper,a linear state feedback control method is used to control the Hopf bifurcation in the model,the corresponding controlled system is generated,and the Hopf bifurcation conditions is derived.Positive and negative feedback control are used to advance or delay Hopf bifurcation,change the type of Hopf bifurcation,eliminate Hopf bifurcation.The numerical results show that the control of Hopf bifurcation is well achieved,which helps to provide certain theoretical support for implementing effective traffic strategies and alleviating traffic congestion.In summary,this paper conducts dynamic analysis and research on macro traffic flow model through phase plane analysis method and bifurcation theory,reveals the nonlinear characteristics,formation mechanisms,laws of traffic state changes of traffic flow phenomena,explores the formation mechanism of stable sudden change behavior and traffic congestion,predicts the stability mutation behavior of the traffic system through bifurcation points,and designs corresponding control schemes for unstable bifurcation points to explore reasonable traffic control methods.So some nonlinear phenomena in the traffic flow are describes and predicts from a new perspective,providing a theoretical basis and scientific decision-making basis for preventing and alleviating traffic congestion.