A high-repetition-rate ytterbium fiber laser, harmonically mode-locked using a phase modulator, is investigated experimentally, numerically, and analytically. Experimental results agree well with numerical simulations using the measured parameter values. By employing a few approximations, our model is cast in terms of a Ginzberg-Landau equation. This equation has known analytic solutions that agree well with the results of the full model in the appropriate limit. Pulse stability is also investigated numerically with an emphasis on the role of third-order dispersion.