标题： 关于兴奋性系统的阈值：基于能量的视角 显示英文标题

标题： On the threshold of excitable systems: An energy-based perspective

摘要： 兴奋性系统的根本特征之一是它们能够表现出不同的亚阈值和超阈值行为。精确量化这一区别需要一个适当的阈值定义，而这一问题在神经动力学中一直难以解决。在本文中，我们基于耗散理论引入了一种针对兴奋性电路的新型能量型阈值定义，具体使用了所需供给的经典概念。根据我们的定义，阈值对应于所需供给的局部最大值，明确区分了亚阈值的被动响应和超阈值的再生性尖峰。我们通过三种典型系统的分析和数值研究（简单RC电路、FitzHugh-Nagumo模型以及生物物理细节丰富的Hodgkin-Huxley模型）展示了并验证了所提出的定义。 显示英文摘要

摘要： A fundamental characteristic of excitable systems is their ability to exhibit distinct subthreshold and suprathreshold behaviors. Precisely quantifying this distinction requires a proper definition of the threshold, which has remained elusive in neurodynamics. In this paper, we introduce a novel, energy-based threshold definition for excitable circuits grounded in dissipativity theory, specifically using the classical concept of required supply. According to our definition, the threshold corresponds to a local maximum of the required supply, clearly separating subthreshold passive responses from suprathreshold regenerative spikes. We illustrate and validate the proposed definition through analytical and numerical studies of three canonical systems: a simple RC circuit, the FitzHugh--Nagumo model, and the biophysically detailed Hodgkin--Huxley model.