Hybrid control of Hopf bifurcation in macroscopic traffic flow: the Little's law-driven continuum model

Continuous traffic flow modeling has attracted significant research attention in recent years. The traditional traffic flow model has obvious shortcomings in describing complex traffic phenomena, particularly in revealing traffic characteristics and bifurcation control. As the basis of service system performance analysis, Little's law is skillfully integrated into macroscopic traffic flow modeling. Currently, the Hopf bifurcation hybrid control method for macroscopic traffic systems remains relatively unknown. Based on the model construction, we further realize the Hopf bifurcation hybrid control, aiming to delay or eliminate the undesired oscillation in the traffic system. The stability condition of the model is derived by the stability analysis method. Furthermore, we have introduced the model's local clustering effect and analyzed each parameter's impact through phase transition analysis. A comparative analysis of similar traffic models has been conducted from the perspectives of speed and density changes. Our results show that the proposed model fits the actual traffic situation and achieves the expected results in the Hopf bifurcation hybrid control of this novel macroscopic traffic model. Through this research, we aim to provide a new idea and method for establishing a continuous traffic flow model and Hopf bifurcation control. We also provide theoretical support and practical guidance for the stability and dynamic behavior control of nonlinear systems.