We present the numerical simulation and experimental results on generation dynamics of an all-fiber holmium laser with an intracavity modulator based on a Mach-Zehnder interferometer. The experimental data were compared with numerical simulation results in a wide range of parameters. An explanation for the observed increase in the pulse repetition rate from 5.8 to 11.6 kHz, as well as the transition to the chaotic pulsations mode, was given. A numerical variation of the unknown or difficult-to-measure losses in the experiment was carried out. The obtained set of parameters allowed us to implement the correct numerical optimization of an active medium and cavity. As a result, the peak powers of about 9.5 and 13 W were obtained during the experiments, as well as in the numerical simulation. (C) 2020 Optical Society of America