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

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
Software:
MATCONT
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