<p>Maglev trains are prone to coupling resonance between the train and the bridge track during operation, and the vehicle bridge coupling system may even experience vibration bifurcation, leading to train instability. To investigate this problem, a periodic time-varying vehicle-bridge coupling vibration model is first developed based on Hamilton’s principle. The Floquet theorem is employed to analyze the stable region of the maglev train and single-span bridge coupling system concerning control parameters. The accuracy of the stability region is validated through numerical simulations. Then, the study extends to investigate the stability of maglev trains passing over multi-span bridges. The vibration bifurcation characteristics of the vehicle-bridge coupling system are analyzed, and the impact of various control parameters on vibration bifurcation is explored. Finally, the resonance problem of maglev trains traversing multi-span bridges is examined, focusing on the relationship between resonant speed and system parameters, as well as strategies to reduce resonant amplitude. Numerical research results demonstrate that a reduction in car body mass and an increase in the aerodynamic lift coefficient cause the stable region of the system’s PD control parameters to shift downward, with the boundary of the stable region representing the critical point for system bifurcation. To suppress bifurcation induced by train vibration, this can be achieved by increasing the current and speed control parameters. Adjusting the current and speed control parameters to keep them away from the bifurcation points can reduce the resonant amplitude of the suspension gap. Adjusting the displacement control parameters to keep them away from the upper bifurcation point can suppress the suspension gap resonance amplitude caused by track disturbances; simultaneously keeping them away from both the upper and lower bifurcation points can mitigate the suspension gap resonance amplitude caused by aerodynamic disturbances.</p>