Bifurcations and limit cycles in a model for a vocal fold oscillator. (English) Zbl 1100.34028

Lucero, Jorge C.

Commun. Math. Sci. 3, No. 4, 517-529 (2005).

The paper investigates the dynamics of a simple mathematical model, recently proposed by Laje, Gardner and Mindlin, that describes the vocal fold oscillation at voice production. Assuming realistic data of the various parameters involved in the underlying autonomous nonlinear second-order ODE, the author determines the type of bifurcation that produces the oscillation, and shows that, particularly after a slight modification of the model, the wellknown phenomenon of oscillation hysteresis may occur. It turns out that the observed pattern of voice onset-offset is produced by a fold or saddle-node bifurcation of limit cycles that for certain values of parameters, originate from a subcritical Hopf bifurcation. This secondary bifurcation was detected only by applying a numerical continuation procedure for the amplitude of the Hopf cycles.

Reviewer: Josef Hainzl (Freiburg)

MSC:

34C15	Nonlinear oscillations and coupled oscillators for ordinary differential equations
37G15	Bifurcations of limit cycles and periodic orbits in dynamical systems
34C55	Hysteresis for ordinary differential equations
34C25	Periodic solutions to ordinary differential equations
92C10	Biomechanics
34C23	Bifurcation theory for ordinary differential equations
34C60	Qualitative investigation and simulation of ordinary differential equation models

Keywords:

Nonlinear oscillator; bifurcation; limit cycle; hysteresis

Software:

MATCONT