Saddle-node bifurcation control of a traffic flow model with multiple preceding vehicles

This paper proposes a macroscopic traffic flow model, combined with the bifurcation theory in nonlinear dynamics, to explore the optimization and control of traffic flow stability under the influence of multiple preceding vehicle information. First, the balance solutions and stability of the multi-leading vehicle information model in an intelligent Internet of Vehicles (IoV) environment are analyzed using differential equation theory. The system’s behavioral patterns are revealed, and the transitions between various traffic states are theoretically characterized. This also describes the simultaneous occurrence of different traffic phenomena and their interrelationships, thus providing a foundation for subsequent research. Next, based on the equilibrium points, the paper investigates the saddle node bifurcation behavior in the traffic system, revealing the influence mechanism of multi-leading vehicle information on the stability of the traffic system and the critical points of system-induced abrupt changes in the IoV environment. The intrinsic mechanisms underlying global stability changes are further discussed. Then, for the unstable saddle-node bifurcation points, a stabilization strategy based on feedback control is proposed. By adjusting density and other parameters, the control parameters are tuned to successfully delay or eliminate the occurrence of unstable bifurcation points, thereby reducing system stability loss and the multiple solution phenomena. Finally, the effectiveness of the model’s bifurcation phenomenon and control method on traffic flow stability is verified by numerical simulation, providing a theoretical basis and practical support for the optimization of the traffic system under the vehicle networking environment. The results offer theoretical support for optimizing intelligent transportation systems and advancing autonomous driving.