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.

中文翻译：

---

重新审视神经“气泡”动力学。

在本文中，我们重新审视了 John G Taylor 在二维神经场模型中的神经“气泡”动力学方面的工作。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. 在这种情况下，定义“气泡”的激发或活跃区域的动力学减少到边界的动力学。John 的工作重点是径向对称“气泡”的特性，包括存在性和径向稳定性，并将其应用于自组织神经网络中的地形图形成理论。除了回顾 John 在该领域的工作外，我们还包括一些最近的结果，这些结果处理更一般的扰动类别。