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.

本文研究了英语和普通话中/b/和/m/的唇收缩轨迹，并发现这种轨迹在语言和语境间普遍表现为位移与速度的瞬时比率遵循指数衰减曲线。文章提出了一个非线性二阶动态系统模型来描述这些轨迹，结果表明该模型可以很好地拟合个体运动轨迹，并为发音运动的动力学提供了新的理论基础，有助于理解声调、运动协调和随机噪声等对发音运动学的影响。

非线性二阶动力学描述跨语言和语境的唇收缩轨迹