<p>To ensure the safe and stable operation of superconducting electrodynamic suspension (EDS) trains, this study analyzes the dynamic stability and safety boundary of the EDS system by numerical method. Firstly, a three-dimensional electromagnetic force calculation model of the superconducting coil and the null-flux coil based on the dynamic circuit theory, mutual inductance formula and virtual displacement method is established, and it is embedded into the equation of motion of the bogie. Secondly, considering the discrete-time characteristic of the EDS system model, an improved algorithm of the Lyapunov exponent based on perturbation theory and QR orthogonal decomposition method is proposed to evaluate the dynamic stability of the EDS system under different initial states. On this basis, the binary search method is used to determine the safety boundary of vertical-lateral motion of the bogie under the suspension failure mode and the physical space constraint, respectively, and the influence of the train running speed and the active damping coil on the safety region is discussed. The results indicate that, although the EDS system exhibits dynamic stability within the explored initial state-space domain, this stability is non-asymptotic, which means that significant disturbances may make the movement trajectory of the maglev vehicle exceed the physical boundary of the track and cause a collision. In addition, the safety region area first increases and then decreases with the increase of train running speed, and the introduction of active damping coil can effectively expand the safety boundary and improve the safety and smoothness of train operation. This study can provide theoretical guidance for the EDS train operation status assessment and safety protection design.</p>