title: Neural 'Bubble' Dynamics Revisited.
abstract: In this paper, we revisit the work of John G Taylor on neural 'bubble' dynamics in two-dimensional neural field models. This builds on original work of Amari in a one-dimensional setting and makes use of the fact that mathematical treatments are much simpler when the firing rate function is chosen to be a Heaviside. In this case, the dynamics of an excited or active region, defining a 'bubble', reduce to the dynamics of the boundary. The focus of John's work was on the properties of radially symmetric 'bubbles', including existence and radial stability, with applications to the theory of topographic map formation in self-organising neural networks. As well as reviewing John's work in this area, we also include some recent results that treat more general classes of perturbations.
authors.affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112 USA.
authors.forename: Paul C
authors.initials: PC
authors.lastname: Bressloff
authors.affiliation: Department of Mathematical Sciences, Center for Mathematical Medicine and Biology, University of Nottingham, Nottingham, NG7 2RD UK.
authors.forename: Stephen
authors.initials: S
authors.lastname: Coombes
keywords: Breathers; Bumps; Neural field models; Self-organisation