Bifurcation analysis for Kuhne's density gradient traffic flow model

The essence of traffic congestion is a kind of bifurcation behavior incurred by the loss of stability in the traffic flow from the perspective of system stability. Therefore, researching the bifurcation characteristics of traffic flow can provide some new methods for relieving the traffic congestion. In this paper, we study the bifurcation dynamic behavior and the bifurcation conditions of traffic flow based on Kuhne's continuum traffic flow model. We discussed the types and stabilities of the equilibrium solutions and proved the existence conditions of some bifurcation of the model. Then various bifurcations of the system are found by numerical simulation and the stability catastrophic behaviors initiated by some bifurcation in traffic flow are investigated. Combined with the measured data, we study the actual traffic flow bifurcation phenomena and analyze the internal reasons for the stability catastrophic behavior of traffic flow passed by the bifurcation point. The nonlinear characteristics and formation mechanism of traffic flow phenomena are revealed from a new perspective. It may help to design the corresponding control schemes for preventing and alleviating traffic congestion.