Modeling of chaotic vibrations in symmetric vocal folds

Abstract

The chaos mechanism of above-range phonation was examined in symmetrically modeled vocal folds by using the traditional two-mass model assumption. The Poincaré map technique was used to display chaotic attractors. This method provided an effective description of irregular vocal-fold movements. The power spectrum, Lyapunov exponent, and Kaplan-Yorke dimension were employed to describe chaotic vibrations in the vocal-fold model. These nonlinear dynamic analyses suggested that, for the positive Lyapunov exponent, chaotic attractors contribute to irregular vocal-fold vibrations. Descriptions of complicated irregular vibrations of the vocal fold yielded evidence of chaos. To investigate the effects of independent parameters such as subglottal pressure, coupling stiffness, and phonation neutral area, bifurcation diagrams based on the Poincaré map were discussed. The results confirmed that the dynamics of the two-mass model was strongly influenced by independent parameters. Nonlinear dynamic methods were expected to provide useful information for better understanding of irregular vocal-fold vibrations as well as of the dynamic mechanism of above-range phonation in excised larynx experimentation.

Dynamics of the Vocal Fold Oscillation

“…Details of these equations may be found in the cited references [3,6,10,9,11,5]. Figure 5 shows simulation results of glottal airflow when varying the subglottal pressure from 0 to a maximum value, and back to zero.…”

“…Using mathematical models of that structure, past works have shown the existence of several nonlinear phenomena, such as multiple equilibrium positions and limit cycles [8,3], several types of bifurcations [8,3,16], and chaotic behavior [3,6]. Our recent work [8,10,9] has considered the dynamics of the onset and offset of the oscillation.…”

Relating pain intensity of newborns to onset of nonlinear phenomena in cry recordings

“…The model represents the vocal cords as a viscoelastic coupled oscillator. There exists a substantial evidence that vocal-fold vibration is a highly nonlinear process [10,20], and the combined effects of nonlinear biomechanical events and aerodynamic events can produce rich irregular vibratory behaviors such as bifurcation and chaos [12]. Furthermore, the two-mass model is able to produce toroidal oscillations and chaotic transitions such as period doubling and Ruelle-Takens-Newhouse.…”

Characterization of chaotic dynamics in the vocalization of Cervus elaphus corsicanus (L)

“…These behaviors can be predicted by theoretical models. For example, the two mass model (the most accepted for mammal apparatus of phonation) can exhibit irregular oscillations [3,4]. The apparatus of phonation can be investigated through the characterization of the animal vocalization, where vocal nonlinearity can be used.…”