Communications in Mathematical Sciences

Volume 3 (2005)

Number 4

Bifurcations and limit cycles in a model for a vocal fold oscillator

Pages: 517 – 529

DOI: http://dx.doi.org/10.4310/CMS.2005.v3.n4.a3

Author

Jorge C. Lucero

Abstract

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.

2010 Mathematics Subject Classification

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

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