Linear and nonlinear stability analysis of a car-following model considering velocity difference of two adjacent lanes

An improved optimal velocity model, which considers the velocity difference of two adjacent lanes, is presented in this paper. Using linear stability theory, the stability criterion of the new model is obtained and the neutral stability curves are plotted. By applying the reductive perturbation method, the nonlinear stability of the proposed model is also investigated and the soliton solution of the modified Korteweg–de Vries equation near the critical point is obtained to characterize the unstable region. All the theoretical analysis and numerical results demonstrate that the proposed model can characterize traffic following behaviors effectively and achieve better stability.