This paper examines an updated version of a lumped mucosal wave model of the vocal fold oscillation during phonation. Threshold values of the subglottal pressure and the mean (DC) glottal airflow for the oscillation onset are determined. Depending on the nonlinear characteristics of the model, an oscillation hysteresis phenomenon may occur, with different values for the oscillation onset and offset threshold. The threshold values depend on the oscillation frequency, but the occurrence of the hysteresis is independent of it. The results are tested against pressure data collected from a mechanical replica of the vocal folds, and oral airflow data collected from speakers producing intervocalic /h/. In the human speech data, observed differences between voice onset and offset may be attributed to variations in voice pitch, with a very small or inexistent hysteresis phenomenon.

This paper analyzes the interaction between the vocal folds and vocal tract at phonation onset due to the acoustical coupling between both systems. Data collected from a mechanical replica of the vocal folds show that changes in vocal tract length induce fluctuations in the oscillation threshold values of both subglottal pressure and frequency. Frequency jumps and maxima of the threshold pressure occur when the oscillation frequency is slightly above a vocal tract resonance. Both the downstream and upstream vocal tracts may produce those same effects. A simple mathematical model is next proposed, based on a lumped description of tissue mechanics, quasi-steady flow and one-dimensional acoustics. The model shows that the frequency jumps are produced by saddle-node bifurcations between limit cycles forming a classical pattern of a cusp catastrophe. The transition from a low frequency oscillation to a high frequency one may be achieved through two different paths: in case of a large acoustical coupling (narrow vocal tract) or high subglottal pressure, the bifurcations are crossed, which causes a frequency jump with a hysteresis loop. By reducing the acoustical coupling (wide vocal tract) or the subglottal pressure, a path around the bifurcations may be followed with a smooth frequency variation.