Animal Gaits [ Back ]

UB - Facultat de Matemàtiques (Aula 2)
Martin Golubitsky
Univ. of Houston


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.

Joint work with Ian Stewart, Luciano Buono and Jim Collins