Port-Hamiltonian Representation of Dynamical Systems. Application to Self-Sustained Oscillations in the Vocal Apparatus
Résumé
Phonation is a natural example of nonlinear dynamical system with self-sustained oscillations, here resulting from the controlled nonlinear coupling between the deformable vocal folds and the airflow expired from the lungs through the glottis and the vocal tract. As a proof of concept, we propose a minimal model of the full vocal apparatus using the port-Hamiltonian representation that emphasises on the structure of a system (on the separation between the behaviour of the subsystems and their interconnection) and on the power exchanges. Numerical results on bifurcations are qualitatively discussed in relation to voice pathologies.
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