Bifurcation analysis and control strategy for a car-following model considering jerk behavior

Abstract

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.