Neural Bubble Dynamics Revisited
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 Johns 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 Johns work in this area, we also include some recent results that treat more general classes of perturbations.
neural field models self-organisation bumps breathers