Simulation Research on Chaos Characteristics of a Class of Macroscopic Traffic Models

Based on a commonly used macroscopic freeway traffic flow model, this paper discusses the application of the model in a road section which has three sections of equal length. Bifurcation and chaos theory of nonlinear dynamical systems are used to calculate the complex nonlinear bifurcation and chaos phenomena in freeway traffic flow. The numerical simulations, including bifurcation diagrams and computation of the maximum Lyapunov exponent, show the rich and complex dynamical behavior and critical phenomena in traffic flow. This paper indicates that the critical bifurcation parameter where the state variables change suddenly can be considered as the maximum service flow of freeway under certain conditions.