Nonlinear second-order dynamics describe labial constriction trajectories across languages and contexts

TL;DR

This study models labial constriction movements in speech as a nonlinear second-order dynamical system, revealing consistent exponential decay patterns across languages and providing a new framework for understanding articulatory kinematics.

Contribution

It introduces a simple, two-parameter nonlinear dynamical model that accurately describes labial constriction trajectories in speech production across languages.

Findings

Model fits individual trajectories well

Simulated trajectories match empirical data

Captures key kinematic variables

Abstract

We investigate the dynamics of labial constriction trajectories during the production of /b/ and /m/ in English and Mandarin. We find that, across languages and contexts, the ratio of instantaneous displacement to instantaneous velocity generally follows an exponential decay curve from movement onset to movement offset. We formalize this empirical discovery in a differential equation and, in combination with an assumption of point attractor dynamics, derive a nonlinear second-order dynamical system describing labial constriction trajectories. The equation has only two parameters, T and r. T corresponds to the target state and r corresponds to movement rapidity. Thus, each of the parameters corresponds to a phonetically relevant dimension of control. Nonlinear regression demonstrates that the model provides excellent fits to individual movement trajectories. Moreover, trajectories simulated from the model qualitatively match empirical trajectories, and capture key kinematic variables like duration, peak velocity, and time to achieve peak velocity. The model constitutes a proposal for the dynamics of individual articulatory movements, and thus offers a novel foundation from which to understand additional influences on articulatory kinematics like prosody, inter-movement coordination, and stochastic noise.