A Dynamical Systems Analysis of Running Cockroaches
Mathematical Biosciences Institute Workshop 4: Neuromechanics of Locomotion, 2008
Abstract
We use methods from dynamical systems theory to analyze movement of /Blaberus discoidalis/ cockroaches. One of our key objectives is to derive dimensionally reduced models that describe the biomechanical synergies used by an animal steadily running on flat ground. By modeling the motion as a stable periodic orbit in a body centered frame of reference, we may apply Floquet theory to the problem. In the absence of noise, the theory predicts a change of coordinates which rectifies the motion transverse to the orbit to a time invariant linear system with modes that decay exponentially. These Floquet modes can be divided into those that are highly damped and those that are weakly damped. Preliminary results give evidence for few weakly damped modes, and for many highly damped modes that decay in less than a stride. We hypothesize that the weakly damped modes form a template for the neuromechanical control of locomotion. We describe our use of diverse tools from motion tracking, numerical analysis, visualization and geometric statistics to fit these periodic orbit models to video recordings of running cockroaches. Our focus is on the numerical estimation of a phase variable and of the linearized first return map, with quantified levels of statistical confidence in the presence of noisy data.
BibTeX
@conference{revzen-2008-MBI,
author = {Revzen, Shai and Guckenheimer, J M},
title = {A Dynamical Systems Analysis of Running Cockroaches},
booktitle = {Mathematical Biosciences Institute Workshop 4: Neuromechanics of Locomotion},
year = {2008},
url = {https://web.archive.org/web/20190129150507/https://mbi.osu.edu/event/?id=69}
}