Bifurcation control of solid angle car-following model through a time-delay feedback method

In order to alleviate unstable factor-caused bifurcation and reduce oscillations in traffic flow, a feedback control with consideration of time delay is designed for the solid angle model (SAM). The stability and bifurcation condition of the new SAM is derived through linear analysis and bifurcation analysis, and then accurate range of stable region is obtained. In order to explore the mechanism of the influence of multiple parameter combinations on the stability of controlled systems, a definite integral stabilization method is provided to determine the stable interval of time delay and feedback gain. Numerical simulations are explored to verify the feasibility and effectiveness of the proposed model, which also demonstrate that feedback gain and delay are two key factors to alleviate traffic congestion in the SAM.