Nonliner Analysis of a Synthesized Optimal Velocity Model for Traffic Flow

We analyze a new car-following model described by a differential-difference equation with a synthesized optimal velocity function (SOVF), which depends on the front interactions between every two adjacent vehicles instead of the weighted average headway. The model is analyzed with the use of the linear stability theory and nonlinear analysis method. The stability and neutral stability condition are obtained. We also derive the modified KdV (Korteweg-de Vries) equation and the kink-antikink soliton solution near the critical point. A simulation is conducted with integrating the differential-difference equation by the Euler scheme. The results of the numerical simulation verify the validity of the new model.