In order to investigate the effect of strong wind on dynamic characteristic of traffic flow, an improved car-following model based on the full velocity difference model is developed in this paper. Wind force is introduced as the influence factor of car-following behavior. Among three components of wind force, lift force and side force are taken into account. The linear stability analysis is carried out and the stability condition of the newly developed model is derived. Numerical analysis is made to explore the effect of strong wind on spatial-time evolution of a small perturbation. The results show that the strong wind can significantly affect the stability of traffic flow. Driving safety in strong wind is also studied by comparing the lateral force under different wind speeds with the side friction of vehicles. Finally, the fuel consumption of vehicle in strong wind condition is explored and the results show that the fuel consumption decreased with the increase of wind speed.
In this paper, a new car-following model considering effect of the driver’s forecast behavior is proposed based on the full velocity difference model (FVDM). Using the new model, we investigate the starting process of the vehicle motion under a traffic signal and find that the delay time of vehicle motion is reduced. Then the stability condition of the new model is derived and the modified Korteweg–de Vries (mKdV) equation is constructed to describe the traffic behavior near the critical point. Numerical simulation is compatible with the analysis of theory such as density wave, hysteresis loop, which shows that the new model is reasonable. The results show that considering the effect of driver’s forecast behavior can help to enhance the stability of traffic flow.
A new bifurcation analysis method for analyzing and predicting the complex nonlinear traffic phenomena based on the macroscopic traffic flow model is presented in this paper. This method makes use of variable substitution to transform a traditional traffic flow model into a new model which is suitable for the stability analysis. Although the substitution seems to be simple, it can extend the range of the variable to infinity and build a relationship between the traffic congestion and the unstable system in the phase plane. So the problem of traffic flow could be converted into that of system stability. The analysis identifies the types and stabilities of the equilibrium solutions of the new model and gives the overall distribution structure of the nearby equilibrium solutions in the phase plane. Then we deduce the existence conditions of the models Hopf bifurcation and saddle-node bifurcation and find some bifurcations such as Hopf bifurcation, saddle-node bifurcation, Limit Point bifurcation of cycles and Bogdanov–Takens bifurcation. Furthermore, the Hopf bifurcation and saddle-node bifurcation are selected as the starting point of density temporal evolution and it will be helpful for improving our understanding of stop-and-go wave and local cluster effects observed in the free-way traffic.
Nonlinear analysis of complex traffic flow systems can provide a deep understanding of the causes of various traffic phenomena and reduce traffic congestion, and bifurcation analysis is a powerful method for it. In this paper, based on the improved Aw-Rascle model, a new macroscopic traffic flow model is proposed, which takes into account the road factors and driver psychological factor in the curve environment which can effectively simulate many realistic traffic phenomena on curves. The macroscopic traffic flow model on curved road is analyzed by bifurcation, firstly, it is transformed into a nonlinear dynamical system, then its stability conditions and the existence conditions of bifurcations are derived, and the changes of trajectories near the equilibrium points are described by phase plane. From an equilibrium point, various bifurcation structures describing the nonlinear traffic flow are obtained. In this paper, the influence of different bifurcations on traffic flow is analyzed, and the causes of special traffic phenomena such as stop-and-go and traffic clustering are described using Hopf bifurcation as the starting point of density temporal evolution. The derivation and simulation show that both road factors and driver psychological factor affect the stability of traffic flow on curves, and the study of bifurcation in the curved traffic flow model provides decision support for traffic management.
This paper studies the stability of a speed gradient continuous traffic flow model, which is proposed by Ge et al and based on TVDM. The nonlinear and linear systems of traveling wave solutions of the model equation are derived by traveling wave substitution. And the types of equilibrium points and it’s stability are analyzed theoretically. Finally, the phase plane diagram is obtained through simulation, and the global distribution structure of the trajectories is analyzed. The results show that the numerical results are consistent with the theoretical analysis, so some nonlinear traffic phenomena can be analyzed and predicted from the perspective of global stability.
This paper proposes a new density gradient continuous traffic flow model, and analyzes the linear stability of the model, as well as the bifurcation type of the model. Numerical simulation of the new model verifies the usability of the model. From the perspective of system stability, the bifurcation analysis method is used to analyze the nonlinear traffic phenomena on the expressway. The equilibrium solution of the model is discussed. On this basis, Hopf bifurcation, saddle bifurcation and Bogdanov–Takens bifurcation are obtained, and the existence conditions and fractional types of Hopf bifurcation and saddle bifurcation are obtained. The traffic flow characteristics of Hopf bifurcation and saddle node bifurcation are analyzed.
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