This article presents an analysis of the dynamics of a bidimensional oscillator, which
has been proposed as a simple model for the vocal fold motion at phonation. The model is capable of
producing an oscillation with physiologically realistic values for the parameters. A simple extension
of the model using even-powered polynomials in the damping factor is proposed, to permit the
occurrence of an oscillation hysteresis phenomenon commonly observed in voice onset-offset patterns.
This phenomenon appears from the combination of a subcritical Hopf bifurcation where an unstable
limit cycle is produced, with a fold bifurcation between limit cycles, where the unstable limit cycle
coalesces and cancels with a stable limit cycle. The results are illustrated with phase plane plots and
bifurcation diagrams obtained using numerical continuation techniques.