UNIVERSITY OF COLORADO AT DENVER

PLACE: Mathematics Conference Room 626 UCD Building, 1250 14th St., Denver

TIME: NOON (Refreshments served at 11:45 am)

DATE: August 25, 2000

Title:
       Oscillations in Coupled Systems and Animal Gaits

Speaker:
       Martin Golubitsky
       Department of Mathematics, University of Houston

Abstract:
Collins and Stewart noted that many quadruped gaits can be
described by spatio-temporal symmetries.  For example, when a
horse paces it moves both left legs in unison and then both
right legs and so on.  The motion is described by two symmetries:
Interchange front and back legs, and swap left and right legs
with a half-period phase shift.

Biologists postulate the existence of a central pattern generator
(CPG) in the neural system that sends periodic signals to the
legs.  CPGs can be thought of as electrical circuits that produce
periodic signals and can be modeled by coupled systems of
differential equations with symmetries based on leg permuation.

In this lecture we discuss animal gaits; describe how periodic
solutions with prescribed spatio-temporal symmetry can be formed
in symmetric systems; construct a CPG architecture that naturally
produces quadrupedal gait rhythms; and make several testable
predictions about gaits.

This research is joint with Ian Stewart, Luciano Buono, and Jim
Collins.