Nonlinear analysis of lattice model with consideration of optimal current difference

Based on Li’s lattice model, a new lattice model considering the influence of optimal current difference information is presented. The linear stability criterion of this model is obtained by employing the linear stability theory. The results show that the new consideration contributes to the stabilization of traffic systems. The modified Korteweg-de Vries (mKdV) equation is derived by using the nonlinear analysis method. The occurrence of traffic jamming transitions could be thus described by the kink-antikink soliton solution for the mKdV equation. From the simulation results of space–time evolution of the vehicle density, it is shown that the traffic jam is suppressed efficiently with considering the information of optimal current difference, and the analytical results is in good agreement with the simulation ones.

► In order to enforce the stability of traffic flow, the influence of optimal current difference information is introduced in the existed lattice model, which has not considerate this factor so far.
► The stable condition of the extended model is put forward.
► By means of the nonlinear analysis, we deduce the mKdV equation near the critical point and obtain its kink-antikink soliton solution to describe the jamming transition.