Nonlinear analysis for an improved car-following model account for the optimal velocity changes with memory

In this paper, an extended car-following model is developed basing on the full velocity difference model (FVDM) to investigate the effect of the optimal velocity changes with memory on traffic flow. The stability conditions of the improved model are obtained through linear stability analysis. Then the time-dependent Ginzburg-Landau (TDGL) equation and the modified Korteweg-de Vries (mKdV) equation are derived by using nonlinear analysis. The kink-antikink soliton can describe the traffic jams near the critical point. Moreover, the evolution of traffic jam and corresponding the change of energy consumption are discussed. Numerical simulations show that the extended model is found not only to enhance the stability of traffic flow but also to depress the energy consumption. The numerical results are in good agreement with the theoretical analysis.