Port-Hamiltonian approach to self-sustained oscillations in the vocal apparatus

Overview & Synopsis

Phonation is a natural example of self-sustained oscillations in a nonlinear dynamical system. It results 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 explore the port-Hamiltonian approach to propose a minimal model of the full vocal apparatus. This port-Hamiltonian theory emphasises on the structure of a system, i.e., on the separation between the behaviour of the subsystems and their assembly, with two essential consequences : the modularity of the approach (enabling improvement in modelling of some subsystem independently of the others) and guaranteed power balance. We here present the minimal model of the vocal apparatus, and compare the time-domain simulations based on the numerical methods designed in the port-Hamiltonian approach, to results on bifurcations obtained by means of continuation methods.