A vehicle model with multiple degrees of freedom is regarded as object of study, which is coupled with tire neural network model. The nonlinear lateral dynamics system is established based on vehicle parameters and the tire data obtained from the transient test on the road rotation test bench. This system has a complicated structure, so it is difficult to obtain the analytical solution. The numerical method can be used to study the intrinsic properties of time sequence of yaw angular velocity and lateral declination with the changes in front wheel angle and the vehicle speed. The simulation results show that this system has a steady-state response tending to the fixed point when the parameters are fixed. Moreover, when system parameters make periodic perturbation with different frequencies, the calculation of power spectrum, bifurcation diagram and largest Lyapunov exponent diagram may provide the conditions and process to keep the system's stability and bifurcation. Meantime, the characteristics of chaotic attractor are analyzed, in order to provide a theoretical reference for the chaos control.