Low dimensional dynamics in biological motor patterns

G B MINDLIN

Topology and Dynamics of Chaos

World Scientific

Lugar: nueva york; Año: 2013; p. 269 - 280

Bob Gilmore leads a beautiful program of research that aims at providing a classification of chaotic dynamics present in natural systems. That program allows to build confidence, or refute models proposed to account for observed complex dynamics. This strategy has been particularly useful for systems whose behavior can be explained in terms of low dimensional dynamical systems. Years after the time I spent with Bob and his coworkers collaborating in that project, I found experimental evidence of low dimensional, non trivial dynamics in the motor patterns used by some songbirds during their vocalizations. This is intriguing, since motor patterns emerge out of the interaction of an enourmous number of individual dynamical units. Under which conditions do large arrays of out of equilibrium units present low dimensional average activity? Is synchronization necessary to achieve these states? Are there other mechanisms leading to low dimensional average dynamics? In this chapter, I review  recent studies on the macroscopic behavior displayed by  a large set of coupled excitable units which are periodically forced. I show that low dimensional, yet non trivial average dynamics emerges  in a regime presenting a time dependent degree of synchrony.