Functional architectures and structured flows on manifolds: a dynamical framework for motor behavior

We outline a dynamical framework for sequential sensorimotor behavior based on the sequential composition of basic behavioral units. Basic units are conceptualized as temporarily existing low-dimensional dynamical objects, or structured flows, emerging from a high-dimensional system, referred to as structured flows on manifolds. Theorems from dynamical system theory allow for the unambiguous classification of behaviors as represented by structured flows, and thus provide a means to define and identify basic units. The ensemble of structured flows available to an individual defines his or her dynamical repertoire. We briefly review experimental evidence that has identified a few basic elements likely to contribute to each individual's repertoire. Complex behavior requires the involvement of a (typically high-dimensional) dynamics operating at a time scale slower than that of the elements in the dynamical repertoire. At any given time, in the competition between units of the repertoire, the slow dynamics temporarily favor the dominance of one element over others in a sequential fashion, binding together the units and generating complex behavior. The time scale separation between the elements of the repertoire and the slow dynamics define a time scale hierarchy, and their ensemble defines a functional architecture. We illustrate the approach with a functional architecture for handwriting as proof of concept and discuss the implications of the framework for motor control.