Applied Mathematics Seminar | Zahra Aminzare, Gait transitions in a phase oscillator model of an insect central pattern generator

MC 6460

Speaker

Dr. Zahra Aminzare
Applied and Computational Mathematics | Princeton University

Title

Gait transitions in a phase oscillator model of an insect central pattern generator 

Abstract

Insect locomotion is an active research area in both biology and engineering. From a mathematical point of view, the interest is to understand the mechanism of central pattern generators (CPGs), networks of neurons in the thoracic and other ganglia, that produce various locomotion patterns.  It has been observed that fast running insects (cockroaches) employ a tripod gait with three legs lifted off the ground simultaneously in swing, while slow walking insects (stick insects) use a tetrapod gait with two legs lifted off the ground simultaneously. Fruit flies use both gaits and exhibit a transition from tetrapod to tripod at intermediate speeds. In this work, we study the effect of stepping frequency on gait transition from tetrapod to tripod in a bursting neuron model in which each cell represents a hemisegmental thoracic circuit of the central pattern generator. Employing phase reduction, we reduce the network of bursting neurons represented by 24 ordinary differential equations to 6 coupled nonlinear phase oscillators, each corresponding to a network controlling one leg. Assuming that the left legs maintain constant phase differences with the right legs (contralateral symmetry), we reduce from 6 equations to 3, allowing analysis of a dynamical system with 2 phase differences defined on a torus. We show that bifurcations occur from multiple stable tetrapod gaits to a unique stable tripod gait as speed increases. Finally, we consider gait transitions in two sets of data filled to freely walking fruit flies.