Based on the Hodgkin–Huxley and Hindmarsh–Rose models, this paper proposes a geometric phenomenological model of bursting neuron in its simplest form, describing the dynamic motion on a mug-shaped branched manifold, which is a cylinder tied to a ribbon. Rigorous mathematical analysis is performed on the nature of the bursting neuron solutions: the number of spikes in a burst, the periodicity or chaoticity of the bursts, etc. The model is then generalized to obtain mixing burst of any number of spikes. Finally, an example is presented to verify the theoretical results.

中文翻译：

---

杯形分支歧管上尖峰和爆发神经元的几何模型

基于 Hodgkin-Huxley 和 Hindmarsh-Rose 模型，本文提出了一种最简单形式的突发神经元的几何唯象模型，描述了杯形分支流形上的动态运动，该流形是一个绑在丝带上的圆柱体。对突发神经元解的性质进行严格的数学分析：突发中的尖峰数量、突发的周期性或混沌性等。然后对该模型进行推广以获得任意数量的尖峰的混合突发。最后给出一个例子来验证理论结果。