Bifurcation analysis of traffic flow on fast and slow lanes

The highway traffic system is a complex, dynamically evolving entity. With the increasing severity of traffic congestion, understanding the behavior of this systems has become a critical area of research. This paper investigates the bifurcation characteristics of traffic flow systems and proposes effective lane-changing rules, providing novel insights for alleviating traffic congestion. Based on real road traffic conditions, the two-lane macroscopic traffic flow model is improved by introducing variables such as memory time, lane-changing coefficients and the fast-slow lanes. Bifurcation analysis of the improved model reveals some critical points of stability within traffic system. Through numerical simulations, the study investigates the impact of memory time and lane-changing coefficients on fuel consumption, and reveals some nonequilibrium phenomena such as instability caused by small disturbance, stop-and-go waves, local clusters and phase transitions phenomena. This indicates a close relationship between the critical point of traffic system stability and bifurcation, revealing the dynamic mechanisms behind the triggering traffic congestion. By modeling the fast-slow lanes traffic flow and conducting bifurcation analysis, this research elucidates the dynamic mechanism of stability in traffic system, providing theoretical support for improving traffic system stability and alleviating traffic congestion.