Nonlinear analysis of the car-following model considering headway changes with memory and backward looking effect

• DOI: 10.1016/j.physa.2020.125303
• Publication Date: 2020-09-19T06:45:29Z
• Authors: Guangyi Ma; Minghui Ma; Shidong Liang; Yansong Wang; Hui Guo
• Keywords: 0502 economics and business; 05 social sciences

Abstract In order to research the effects of headway changes with memory and backward looking effect on traffic flow, in the light of the full velocity difference model (FVDM), a novel car-following model that considers backward looking effect and headway changes with memory is proposed. The use of linear stability theory is to obtain the stability criterion that can judge traffic flow stability. In addition, on the basis of nonlinear theory, the time-dependent Ginzburg–Lan (TDGL) equation and the modified Korteweg–de Vries (mKdV) equation near the critical stability point are inferred. The kink–antikink solutions of the above two equations can be used to describe the traffic jam. In the end, numerical simulation is carried out, and the results further demonstrate that the novel model can stabilize traffic flow and eliminate traffic jam better.