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To explore the relationship between the dynamic model parameters of a stabilizing device coupled system and the quality status of a ballast bed, this study establishes a dynamic model of a frame-stabilizing device-rail sleeper system by combining track coupling dynamics with the operating mechanism of a stabilizing device and by using the lumped parameter method. Moreover, by combining the experimental results and nonlinear least squares identification method based on the trust-region reflective algorithm, the mapping relationship between the model parameters and the lateral resistance of the sleeper is discussed. In addition, the dynamic model is validated by numerical simulation using the fourth-order Runge-Kutta method. Results show that the model has good accuracy, and the acceleration peak error rates between the dynamic model response and the test data are all within 5 %; the lateral resistance of the sleeper is positively and negatively correlated with the transverse stiffness and transverse damping of the ballast bed in the system model, and the correlation coefficients are 0.96 and 0.89, respectively. [ABSTRACT FROM AUTHOR]