A new car-following model with consideration of the velocity difference between the current speed and the historical speed of the leading car

In this study, a new car-following model is proposed based on taking the effect of the leading vehicle's velocity difference between the current speed and the historical speed into account. The model's linear stability condition is obtained via the linear stability theory. The time-dependent Ginzburg-Landau (TDGL) equation and the modified Korteweg-de Vries (mKdV) equation are deduced through the nonlinear analysis. The kink-antikink soliton can interpret the traffic jams near the critical point. In addition, the connection between the TDGL and the mKdV equations is also given. Numerical simulation shows that the new model can improve the stability of traffic flow, which is consistent with the theoretical analysis correspondingly.