Modeling vocal fold asymmetries with coupled van der Pol oscillators

Abstract

Models of the glottal sound source are being developed to extend a recent synthesizer of disordered voices [Fraj et al., J. Acoust. Soc. Am. 132, 2603-2615(2012]. The synthesizer was based on a nonlinear wave-shaping algorithm which generates a glottal excitation to a concatenated-tube representation of the trachea and vocal tract. The purpose of the present work is to incorporate a physics-based model of the vibrating vocal folds in order to increase the anatomical fidelity of the synthesizer. Further, the model will permit to characterize left-right fold asymmetries and explore the effect of those asymmetries on the resultant vocal timbre. In this report, the vocal folds are represented as a system of two coupled Van der Pol oscillators with noise terms and a detuning factor between their natural frequencies. Regions of phase locked and unlocked oscillations are determined and illustrated with bifurcation diagrams. Also, the effect of frequency detuning on the resultant frequency jitter is analyzed. The results are discussed in terms of their implications for modeling abnormal vocal fold behavior. [Work supported by CNPq (Brazil) and FNRS (Belgium)].

Asynchronous and synchronous quenching of a globally unstable jet via axisymmetry breaking

“…One of the simplest low-dimensional models with self-excited temporal solutions is the VDP oscillator (van der Pol 1926). This model has been used throughout science and engineering to study various nonlinear phenomena (Pikovsky et al 2003;Balanov et al 2009), such as the frictional dynamics of tectonic plates (Cartwright et al 1999), the interaction between vocal folds (Lucero & Schoentgen 2013), and thermoacoustic instabilities in combustors (Noiray & Schuermans 2013a;Guan et al 2019aGuan et al ,b, 2021. Similarly, the forced VDP oscillator has been shown to be able to capture phenomenologically the forced synchronization dynamics of various globally unstable flows, such as cylinder wakes (Baek & Sung 2000), jet diffusion flames (Li & Juniper 2013b) and low-density jets (Li & Juniper 2013a,c).…”

Speech-Based Parameter Estimation of an Asymmetric Vocal Fold Oscillation Model and its Application in Discriminating Vocal Fold Pathologies

“…To model phonation, computational models of vocal folds have been developed, including four broad types: 1-mass models e.g. [11], 2-mass models e.g. [5,10], multi-mass models [13], and finite element models [12].…”

“…The exact physics of the airflow through the glottis during phonation is well studied, e.g., [4,5,6,7,8,9], and a number of physical models have been proposed for it e.g., [5,10,11,12,13,14,15,16]. The models use measured bio-mechanical properties of the vocal folds within a set of equations which capture the movements of the glottis during phonation.…”

Nonlinear dynamics in the study of birdsong

“…It is a hypothesis that deserves to be inspected with care, since the two labia will in general be different, and it has been shown to enrich the dynamics. 22,23 In the case of oscine birds, the syrinx is a bipartite structure, and each of the two sound sources is itself asymmetric: the lateral and medial labia are slightly different. Even in birds with a tracheal syrinx (only one sound source, consisting of two opposed labia at the trachea), the labia are not identical.…”