The two-dimensional neuron model can not only reproduce abundant firing patterns, but also satisfy the research of dynamical behavior because of its nonlinear characteristics. It is the most simplified model that includes the fast and slow variables required for neuron firing. In this paper, the dynamic characteristics of two-dimensional neuron model are described by both analytical and numerical methods, and the influence of model parameters and external stimuli on dynamic characteristics is described. The firing characteristics of the Prescott model under external electrical stimulation are studied, and the influence of electrophysiological parameters on the firing characteristics is analyzed. The saddle-node bifurcation and Hopf bifurcation characteristics are studied through the distribution of equilibrium points. It is found that there are critical saddle-node bifurcation and critical Hopf bifurcation in the Prescott model. And the value range of the key parameters that cause the critical bifurcation of the model is obtained by analytical methods.

中文翻译：

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电刺激下二维神经元模型的分岔分析

二维神经元模型不仅可以再现丰富的放电模式，而且由于其非线性特性，可以满足动力学行为的研究。它是最简化的模型，包括神经元放电所需的快速和慢速变量。本文采用解析和数值方法描述二维神经元模型的动态特性，描述模型参数和外部刺激对动态特性的影响。研究了外部电刺激下Prescott模型的放电特性，分析了电生理参数对放电特性的影响。通过平衡点的分布研究了鞍点分岔和Hopf分岔特性。发现Prescott模型中存在临界鞍点分岔和临界Hopf分岔。并通过解析方法得到引起模型临界分叉的关键参数的取值范围。