Spontaneous oscillations in a variety of systems, including neurons, electrochemical, and semiconductor devices, occur as a consequence of Hopf bifurcation in which the system makes a sudden transition to an unstable dynamical state by the smooth change of a parameter. We review the linear stability analysis of oscillatory systems that operate by current–voltage control using the method of impedance spectroscopy. Based on a general minimal model that contains a fast-destabilizing variable and a slow stabilizing variable, a set of characteristic frequencies that determine the shape of the spectra and the associated dynamical regimes are derived. We apply this method to several self-sustained rhythmic oscillations in the FitzHugh–Nagumo neuron, the Koper–Sluyters electrocatalytic system, and potentiostatic oscillations of a semiconductor device. There is a deep and physically grounded analogy between different oscillating systems: neurons, electrochemical, and semiconductor devices, as they are controlled by similar fundamental processes unified in the equivalent circuit representation. The unique impedance spectroscopic criteria for widely different variables and materials across several fields provide insight into the dynamical properties and enable the investigation of new systems such as artificial neurons for neuromorphic computation.

中文翻译：

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通过阻抗谱分析电化学、神经元和半导体系统中的 Hopf 分岔

各种系统（包括神经元、电化学和半导体设备）中的自发振荡是 Hopf 分岔的结果，在该分岔中，系统通过参数的平滑变化突然过渡到不稳定的动态状态。我们回顾了使用阻抗谱方法通过电流-电压控制运行的振荡系统的线性稳定性分析。基于包含一个快速失稳变量和一个慢速稳定变量的一般最小模型，导出了一组确定光谱形状和相关动力学机制的特征频率。我们将这种方法应用于 FitzHugh-Nagumo 神经元、Koper-Sluyters 电催化系统和半导体器件的恒电位振荡中的几种自持节律振荡。不同的振荡系统之间存在着深刻的物理基础类比：神经元、电化学和半导体设备，因为它们由统一在等效电路表示中的类似基本过程控制。跨多个领域的广泛不同变量和材料的独特阻抗光谱标准提供了对动力学特性的洞察力，并使研究新系统（例如用于神经形态计算的人工神经元）成为可能。