Scaling laws for nonlinear dynamical models of articulatory control

Dynamical theories of speech use computational models of articulatory control to generate quantitative predictions and advance understanding of speech dynamics. The addition of a nonlinear restoring force to task dynamic models is a significant improvement over linear models, but nonlinearity introduces challenges with parameterization and interpretability. We illustrate these problems through numerical simulations and introduce solutions in the form of scaling laws. We apply the scaling laws to a cubic model and show how they facilitate interpretable simulations of articulatory dynamics, and can be theoretically interpreted as imposing physical and cognitive constraints on models of speech movement dynamics.