Lateral Multi-feedback Traffic Flow Modeling And Bifurcation Control

With rapid economic and social development,traffic flow and demand are increasing exponentially,and the complexity of the traffic road network is also rising.In order to build a "double-carbon" society,improve the utilization of road resources and transport efficiency,and break the various bottlenecks encountered in the original traffic network,we need to analyse the causes of traffic congestion in depth and find solutions to various traffic problems.The essence of traffic congestion is an unstable bifurcation phenomenon induced by various complex reasons.When the traffic system passes certain critical bifurcation points,the qualitative state of the system will change abruptly,resulting in a loss of traffic stability.In this paper,based on the use of bifurcation analysis methods,two types of traverse feedback models are established,bifurcation control theory is introduced,and various phase change phenomena existing in the traffic system are combined to summarize the logical laws of traffic flow changes,explore the essential principles,and correlate the special parameters in the traffic modelling process with the unstable changes in the numerical analysis process.The works of this paper are as follows:(1)A macroscopic traffic flow model is developed for this factor of lateral safety feedback,and the model is investigated by means of bifurcation analysis.Using the approximate regression method or Taylor expansion method,isolated wave approximation solutions of the higher order model can be obtained.The type and stability of the equilibrium solutions of the model are discussed using the qualitative theory of differential equations,and the structure of the global distribution of the tracks in the phase plane is analyzed.In addition,the density-wave stability conditions of the model,the saddle-junction bifurcation conditions,and the isolated-wave solutions in the sub-stable region are derived using the approximate regression method.(2)To address the characteristics of the randomness of traffic flow in roads,a transverse compensation feedback model is introduced from the perspective of random functions and applied to the traffic model,and a bifurcation control study is proposed for it.Based on the stochastic function of the lateral compensation model,the Hopf bifurcation phenomenon and Hopf bifurcation control are studied.Firstly,the conditions for the existence of Hopf bifurcation at the equilibrium point in the model are proved theoretically.Then,a feedback controller is designed to control the Hopf bifurcation and the magnitude of the limit loop formed by the Hopf bifurcation.That is,the feedback controller is designed to modify the bifurcation characteristics of the system to adjust the appearance of the system’s equilibrium point to move forward,backward or disappear in order to prevent or alleviate traffic congestion.Finally,the correctness of the results is verified by numerical simulation.(3)The two types of lateral feedback model traffic flow models above are analyzed in depth,and the theoretical analysis is validated by using such models as experimental cases combined with actual traffic data.Using the video of the traffic flow on the North Binhe Road in Lanzhou City,the data on the average density,average flow rate and travelling wave speed of the vehicles on the road were obtained,and the data were used to verify the theoretical analysis of the saddle junction bifurcation and Hopf bifurcation,and the correspondence between the change in traffic state and the above two types of bifurcation was found.