Bifurcation Analysis of the Macroscopic Traffic Flow Model Based on Driver’s Anticipation and Traffic Jerk Effect

Based on realistic traffic conditions, the macroscopic traffic flow model that considers the driver’s anticipation and traffic jerk effect is improved, and the bifurcation theory is used to describe and predict nonlinear traffic phenomena on the road from the perspective of global stability. Firstly, the linear stability conditions and the Korteweg–de Vries–Burgers equation are derived using linear and nonlinear methods to characterize the evolution of traffic flow. The type and stability of the equilibrium solution are discussed using the bifurcation analysis method, and the conditions of existence of the Hopf bifurcation and saddle-node bifurcation are proved. Numerical simulations show that the model can describe the complex nonlinear dynamic phenomena observed on the road. The bifurcation analysis will be helpful for improving our understanding of stop-and-go and sudden changes in stability in real traffic flow.