Communications in Mathematical Sciences

Oscillation region of a piecewise-smooth model of the vocal folds

Cristiane A. Gajo and Jorge C. Lucero

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The two-mass model of the vocal folds is a popular representation of their dynamical structure used in phonation studies. This paper presents an analysis of a recent piecewise-smooth version of the model. This version has two equilibrium positions, and in one of them (the initial prephonatory position) the system is nondifferentiable. Standard methods of stability analysis do not apply for that position, because they require smoothness of the system. A geometrical approach is applied instead, which is an extension of a method previously developed for planar systems. The analysis shows the existence of a transcritical bifurcation between the equilibrium positions, and a Hopf bifurcation related to each of them. The oscillation region of the model is next determined as the area delimited by the Hopf bifurcations. The results are illustrated by a bifurcation diagram and trajectory plots.

Article information

Commun. Math. Sci., Volume 4, Number 2 (2006), 453-469.

First available in Project Euclid: 3 August 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34C15: Nonlinear oscillations, coupled oscillators
Secondary: 34C23: Bifurcation [See also 37Gxx] 34C60: Qualitative investigation and simulation of models 70K42: Equilibria and periodic trajectories 74L15: Biomechanical solid mechanics [See also 92C10] 92C20: Neural biology


Lucero, Jorge C.; Gajo, Cristiane A. Oscillation region of a piecewise-smooth model of the vocal folds. Commun. Math. Sci. 4 (2006), no. 2, 453--469.

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