Gait Transitions in a Phase Oscillator Model of an Insect Central Pattern Generator

Abstract

Legged locomotion involves various gaits. 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. Here we study the effect of stepping frequency on gait transition in an ion-channel bursting neuron model in which each cell represents a hemisegmental thoracic circuit of the central pattern generator. Employing phase reduction, we collapse the network of bursting neurons represented by 24 ordinary differential equations to 6 coupled nonlinear phase oscillators, each corresponding to a subnetwork of neurons controlling one leg. Assuming that the left and right legs maintain constant phase differences (contralateral symmetry), we reduce from 6 equations to 3, allowing analysis of a dynamical system with 2 phase...