Study of behavioral transitions in the traffic system under honking environment

In recent years, the research on the bifurcation of complex nonlinear systems has become more and more extensive. To effectively predict the stability of roadway congestion or traffic flow under specified conditions, studying the bifurcation characteristics of the traffic system and analyzing its internal mechanism for unstable bifurcation points is increasingly essential. This paper transforms the honk-based microscopic model into a macroscopic stability analysis model, investigating the bifurcation characteristics, traffic evolution near equilibrium and bifurcation points, and their potential impact on overall traffic flow. The qualitative analysis of differential equations is employed to delve into the classification and stability characteristics of the equilibrium point within the model, and the existence conditions of Bogdanov-Takens (BT), Cusp (CP), and other bifurcations of the traffic system are proved. The theory of nonlinear system bifurcations informs our analysis of traffic flow evolution, exploring the impact of honking on this process while considering the system's holistic stability, which provides a criterion for preventing and alleviating traffic congestion. This study employs bifurcation analysis to determine the conditions of diverse branching junctures and dynamics within the traffic network. The employment of bifurcation theory sheds light on the sudden shifts in system stability emanating from these critical points, concurrently offering an intricate dissection of the nuanced dynamical behaviors exhibited by parametric dynamic systems. Theoretical and experimental data confirm the bifurcation characteristics of the model in this paper, which provides a data basis for the traffic system to a certain extent.