Bifurcation analysis of a new stochastic traffic flow model

Abstract

Abstract The stochastic function describing the stochastic behavior of traffic flow in the process of acceleration or deceleration can better capture the stochastic characteristics of traffic flow. Based on this, we introduce the stochastic function into a high-order viscous continuous traffic flow model and propose a stochastic traffic flow model. Furthermore, we performed the bifurcation analysis of traffic flow system based on the model. Accordingly, the traffic flow problem is transformed into the stability analysis problem of the system, highlighting the unstable traffic characteristics such as congestion. The model can be used to study the nonlinear dynamic behavior of traffic flow. Based on this model, the existence of Hopf bifurcation and the saddle-node bifurcation is theoretically proved. And the type of the Hopf bifurcation is theoretically derived. The model can also be used to study the mutation behavior of system stability at bifurcation point. From the density space-time diagram of the system, we find that the system undergoes a stability mutation when it passes through the bifurcation point, which is consistent with the theoretical analysis results.