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In order to formulate the relationship between vehicle state responses and tire stiffness, a 4-D nonlinear vehicle lateral dynamic system consisting of roll and planar motions was founded by utilizing a quadratic tire model. Then the 4-D nonlinear system has been simplified to the center manifold to a one order system with the center manifold theory. The stability characteristics in symmetrical and μ-split road conditions were analyzed by bifurcation theory and time-domain simulations. The results demonstrated that the singular point corresponded to the critical state where if bifurcation occurred the vehicle would lose stability. So the vehicle stability at the critical conditions could be improved by changing the front wheel steering angle and it would be a new idea to combine the bifurcation theory and the active steering control technique.