Meeting Abstract

20.3  Sunday, Jan. 4  Study of Neuromechanical Control of Rhythmic Behaviors by Floquet Analysis REVZEN, S*; GUCKENHEIMER, J.M.; FULL, R.J.; Univ. of California, Berkeley CA; Cornell Univ., Ithaca NY; Univ. of California, Berkeley CA shrevz@berkeley.edu

The control of rhythmic behaviors like locomotion is challenging to study when compared with control of fixed-point behaviors such as standing. In rhythmic behaviors perturbations away from the typical cycle may have counter-intuitive consequences later in the same cycle or even several cycles in the future. These causal relationships between seemingly different perturbations at different phases of motion can make predictions drawn from PCA and other matrix factorization methods ineffective. Dynamical systems theory describes the interrelation of perturbations in different parts of a cycle using Floquet Theory. The theory guarantees the existence of a change of coordinates that rectifies the dynamics to the simple linear form found in fixed-point systems. We developed our method for estimating a Floquet structure from kinematics to test the Templates and Anchors Hypothesis. This hypothesis states that rapid locomotion is controlled by restricting the many degrees of freedom of the animal’s morphology, as represented by an "anchored" model, to follow low dimensional "template" dynamics. The presence of a template would express itself in the Floquet structure as having a few weakly damped modes that decay over multiple strides and span the template, and many strongly damped modes that decay within a stride or a step, and span the remainder of the degrees of freedom of the anchor. Our preliminary results suggest that running death’s-head cockroaches, (Blaberus discoidalis), posses a template that can be distinguished in the Floquet structure of the animals’ kinematics. Our methodology can be applied to the study of neuromechanical control in a broad range of rhythmic behaviors. Supported by NSF FIBR.