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Oscillations in Coupled Systems and Animal Gaits
by
Martin Golubitsky
University of Houston
Coauthors: Ian Stewart (University of Warwick), Luciano Buono (University of Warwick), James J. Collins (Boston University)
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.
Date received: January 25, 2000
Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # cady-11.