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This paper aims to studying how to solve dynamic Sylvester quaternion matrix equation (DSQME) using the neural dynamic method. In order to solve the DSQME, the complex representation method is firstly adopted to derive the equivalent dynamic Sylvester complex matrix equation (DSCME) from the DSQME. It is proved that the solution to the DSCME is the same with that of the DSQME in essence. Then, a state-of-the-art neural dynamic method is presented to generate a general dynamic-varying parameter zeroing neural network (DVPZNN) model with its global stability being guaranteed by Lyapunov theory. Specifically, when the linear activation function is utilized in the DVPZNN model, the corresponding model (termed LDVPZNN) achieves finite-time convergence, and time range is theoretically calculated. When the nonlinear powersigmoid activation function is utilized in the DVPZNN model, the corresponding model (termed PSDVPZNN) achieves the better convergence as compared with the LDVPZNN model, which is proved in detail. At last, three examples are presented to compare the solution performance of different neural models for the DSQME and the equivalent DSCME, and the results verify the correctness of the theories, and the superiority of the proposed two DVPZNN models.

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