University of Warwick, UK
Title: Stable Synchronous Propagation in Feedforward Networks for Biped Locomotion
Abstract: Rhythmic gait patterns in animal locomotion are widely believed to be produced by a central pattern generator (CPG), a network of neurons that drives the muscle groups. In joint with with Ian Stewart we have discussed how phase-synchronous signals can propagate along chains of neurons using a feedforward lift of the CPG and, given sufficient conditions for stability to synchrony-breaking perturbations. Here we apply these ideas to biped locomotion. The CPG concerned was introduced by Carla Pinto and Martin Golubitsky. Feedforward architecture propagates the phase pattern of a CPG along a chain of identical modules. For certain rate models, we give analytic conditions that are sufficient for transverse Liapunov and Floquet stability.
Bio: Reader at the Mathematics Institute, University of Warwick. Interests in dynamics of networks with symmetry with a focus on modelling of central pattern generators (in particular hexapod locomotion). Also a long time involvement in industrial applications of mathematics through a stint at OCIAM (Oxford University) and the European Study Groups with Industry. Keeping the legacies of Ian Stewart and Christopher Zeeman alive at Warwick through a popular final year undergraduate module “Bifurcations, Catastrophes and Symmetry”.