Bifurcation Analysis And Control Research Based On Multiple Speed Difference Traffic Flow Model

The branch analysis method is an important method to study the mechanism of traffic congestion action.Branch control is an important tool to alleviate traffic congestion.Since the driver can obtain the speed difference of multiple vehicles in front and behind in advance in the intelligent traffic environment,the information of multiple speed differences will have an impact on the driving behavior of the driver.Therefore,take into concideration the influence of multiple speed differences in the intelligent traffic environment,making branching analysis based on the macroscopic dual speed difference model and macroscopic full speed difference model,Analyze complex traffic phenomena such as stop-and-go and sudden stability changes from a global perspective.Meanwhile,branching control based on the macroscopic dual velocity difference model is carried out by introducing a stochastic function,starting from the branching phenomenon caused by the stochastic behavior,i.e.,by designing a feedback controller to modify the branching characteristics of a given nonlinear system,which can be used to control the happening of Hopf branches.The branching analysis and control study by multi-speed differential traffic flow model can not only improve the traffic condition but also has important significance for reducing congestion.The focus of this paper is as follows:(1)Branching analysis based on the macroscopic two-speed difference model is performed to highlight the sudden change in stability phenomena such as traffic congestion from a macroscopic perspective.First,by using the linear stability analysis method,the shock wave stability condition of the model can be obtained.Then,by using the approximate regression method or by using the Taylor expansion method,isolated wave approximation solutions in the sub-stable region of the macroscopic two-velocity difference model can be obtained.Finally,by using the branching analysis method,the type and stability of the equilibrium point are discussed,and the simulation of the system density spatiotemporal and phase plane diagrams are performed,starting with the saddle junction branching point.The changes in branch points are investigated by numerical simulation analysis,which reproduces complex traffic phenomena such as stop-and-go and sudden changes of stability,which are helpful for studying the intrinsic mechanism of traffic congestion and solving traffic congestion.(2)Considering the influence of intelligent traffic environment,drivers can obtain the speed difference between front and rear multi-vehicles in advance,and improve the full speed variation model to obtain a macroscopic full speed variation model,meanwhile,the phenomenon of unexpected change of macroscopic traffic flow model has been investigated under intelligent traffic environment.First,the effect of multiple speed differences on the traffic flow model in the intelligent traffic environment is considered,and the microscopic full-speed difference model is improved to obtain a new macroscopic full-speed difference model.Then,the type and stability of the model equilibrium point are discussed using the branching analysis method,the condition of the existence of saddle-node branching is proved,and the simulation of the spatiotemporal and phase plane diagrams of the system density is carried out with the saddle-node branching as the starting point,and these simulation diagrams show the state of the system evolution.Finally,through simulations,the newly proposed model reproduces complex traffic phenomena in the intelligent traffic environment,such as stop-and-go and stability abrupt changes,and at the same time,can describe and predict the abrupt change phenomena of traffic flow from a holistic perspective.(3)Hopf branching control research based on the macroscopic dual speed difference model is carried out to realize the delay or disappearance of Hopf branching points,thus relieving traffic congestion.Based on the macroscopic two-velocity difference model,stochastic control functions are incorporated,i.e.,the branching characteristics of the system are changed by the designed feedback controller,such as the location where the equilibrium point appears in the control system,to prevent or alleviate traffic congestion.Finally,the density spatiotemporal and phase plane diagrams are obtained by numerical simulation to observe the stability changes of the dual speed difference model under control while the Hopf branch point control is realized.The study shows that by adjusting the values of the control parameters in the controlled system,the delayed branch point can be achieved,which is helpful for the construction of traffic infrastructure,the setting of traffic rules,and the prediction of traffic accidents.