Modeling transient behaviour in vocal fold vibration using bifurcating nonlinear ordinary differential equation systems

Transient behaviour in the human voice is discussed, with particular reference to pitch breaks. Several nonlinear models for vocal fold vibration are proposed and discussed. One particular pitch break where a triple period emerges out of a double period — and vice versa — is modeled with a simple third order system similar to the Rössler system. For a given parameter value, the proposed model system has two intertwined attractors, one with a double and the other with a triple period. A model system more closely related to the physics of the vocal folds and the laryngograph Lx signal is also proposed. The possibilities of producing pitch breaks with this system are discussed, with particular attention to the hypothesis that pitch breaks are due to a constriction of the airflow above the vocal folds.