Oscillation region of a piecewise-smooth model of the vocal folds. (English) Zbl 1111.92005

Lucero, Jorge C.; Gajo, Cristiane A.

Commun. Math. Sci. 4, No. 2, 453-469 (2006).

Summary: The two-mass model of 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.

MSC:

92C05	Biophysics
34C60	Qualitative investigation and simulation of ordinary differential equation models
76G25	General aerodynamics and subsonic flows
92C10	Biomechanics
70K42	Equilibria and periodic trajectories for nonlinear problems in mechanics
37N25	Dynamical systems in biology