Open Access
December 2005 Bifurcations and limit cycles in a model for a vocal fold oscillator
Jorge C. Lucero
Commun. Math. Sci. 3(4): 517-529 (December 2005).


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.


Download Citation

Jorge C. Lucero. "Bifurcations and limit cycles in a model for a vocal fold oscillator." Commun. Math. Sci. 3 (4) 517 - 529, December 2005.


Published: December 2005
First available in Project Euclid: 7 April 2006

zbMATH: 1100.34028
MathSciNet: MR2188681

Primary: 34C15
Secondary: 34C23 , 34C25 , 37G15 , 74L15 , 92C10

Rights: Copyright © 2005 International Press of Boston

Vol.3 • No. 4 • December 2005
Back to Top