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The study of traffic flow bifurcation control analysis is of great significance for understanding the essential evolution law of traffic flow, controlling traffic flow with practical means and alleviating traffic congestion. This paper describes the influence of lateral distance compensation in the process of lane change, and adjusts the traffic flow from the perspective of bifurcation control, which can capture the characteristics of traffic flow better, so as to describe the practical significance of the actual traffic phenomenon better. For example, the green ratio of traffic lights in the road, the planning and design of traffic signs, and the guidance of traffic condition prediction in ITS. In addition, the traffic flow is introduced and applied to the traffic model from the perspective of random function, and the bifurcation control is carried out according to the bifurcation behavior in traffic. That is, the bifurcation characteristics of the system are modified by the designed feedback controller, and the appearance of the equilibrium point of the system is adjusted to make it move forward, backward or disappear, so as to prevent or alleviate traffic congestion. There are few researches on bifurcation control of traffic flow model with lateral distance compensation. This paper introduces stochastic function based on lateral compensation model to study Hopf bifurcation phenomenon and Hopf bifurcation control. Firstly, the existence condition of Hopf bifurcation at the equilibrium point in the model is proved theoretically. Then, a feedback controller is designed to control the amplitudes of the Hopf bifurcation and the limit cycles formed by the Hopf bifurcation. Finally, the theoretical results are verified by numerical simulation. The research shows that by adjusting the control parameters in the feedback controller, the influence of boundary conditions on the stability of the traffic system is fully described, the effect of unstable focus and saddle point on the system is inhibited, and the traffic flow is slowed down. In addition, the unstable bifurcation points can be eliminated, and the amplitude of the limit cycle formed by Hopf bifurcation can be adjusted, so as to achieve the stability of the control system. • A new continuum model is proposed taking into account the lateral offset compensation. • Introducing the traffic flow into the traffic model from the perspective of the random function. • The designed feedback controller corrects the bifurcation characteristics of the system and adjusts the appearance of the balance point of the system to make it forward, backward or disappear, so as to prevent or reduce traffic jams. [ABSTRACT FROM AUTHOR]

To further improve the adaptability of the optimal velocity model (OVM) in the actual traffic flow, this paper proposes a car-following model that considers both the jerk effect and time-delayed feedback control. To study the dynamic behavior of this model, the following analysis is carried out: A stability conditions and equilibrium points controlling OVM are obtained by stability analysis and Hopf bifurcation analysis; Using the intuitive and accurate definite integral stabilization method (DIS), by calculating the number of all unstable eigenvalues of the characteristic equation, we obtain a stable time-delayed interval, and a time-delayed feedback controller is designed to stabilize the traffic system. The results show that the time-delayed feedback controller expands stable time-delayed interval, suppresses the influence of unstable factors on the traffic system, and improves stability of vehicle traffic; Numerical simulations agree with the theoretical results, indicating that the time-delayed feedback controller can effectively suppress traffic congestion and control the managed traffic. • To further improve the control adaptability of the optimal velocity model (OVM), a car-following model with time-delayed feedback control considering the jerk effect is proposed. • The stability condition and equilibrium points controlling OVM are obtained by stability analysis and Hopf bifurcation analysis. Using the intuitive and accurate definite integral stabilization method (DIS), a stable time-delayed interval is derived by calculating the number of all unstable eigenvalues of the characteristic equation. A time-delayed feedback controller is successfully designed to stabilize the traffic system. • Numerical simulations agree with the theoretical analyses, indicating that the time-delayed feedback controller can effectively suppress traffic congestion to realize the control of traffic flow. [ABSTRACT FROM AUTHOR]