In order to study the nonlinear vibration of the electric wheeled vehicle system under the pavementmagnetic excitation and to excavate the global dynamic information of the system under the synergistic effect of parameters and initial conditions, a new nonsmooth nonlinear timevarying dynamic model of the two-degree-of-freedom 1/4 vertical vibration of an electric wheeled vehicle system including the nonlinear spring force and damping of the suspension system and tires are established. Complex external excitation models with harmonicity, randomness and periodicity are obtained by considering the harmonicity and randomness of road excitation and the piecewise periodicity of electromagnetic excitation. The influence of the correlation between motor speed and multiple initial values on the coexistence behavior of the system and its bifurcation is analyzed. The diversity of coexisting motions and the topology of their basins of attraction are investigated. The mechanism of the influence of rotational speed on the global dynamic stability of the system is revealed. The results show that the synergistic effect of the motor speed and the multiple initial values induces a variety of coexisting motions in the system. The topological structures of the basins of attraction of coexisting motions are complex and diverse, and the vibration amplitude of some coexisting motions may be large or small, and their global dynamic stability changes greatly. The impact of the synergistic effect of the motor speed and the initial value on the nonlinear vibration and global dynamics of the system cannot be ignored. This research has important theoretical significance and engineering value for the dynamic performance improvement and structural optimization of the electric wheel vehicle system.