单离子通道神经元电路的动力学分析方法  

Dynamic analysis method of single ion channel neuron circuit

作　　者：杨梓悦 吴静[1] 李乐桐 YANG Ziyue;WU Jing;LI Letong(School of Automation Science and Electrical Engineering,Beihang University,Beijing 100191,China)

机构地区：[1]北京航空航天大学自动化科学与电气工程学院,北京100191

出　　处：《北京航空航天大学学报》2025年第3期985-991,共7页Journal of Beijing University of Aeronautics and Astronautics

基　　金：北京市自然科学基金(Z220017)。

摘　　要：神经网络是由大量神经元通过突触联结而成的复杂网络系统,神经元的合理建模与分析是理解神经网络的功能及动力学特征的关键,对于推动脑科学与类脑科学研究具有重要价值。利用细胞膜电容和钾离子忆阻器分别表征神经元对电荷的存储和记忆特性,在Hodgkin-Huxley单离子通道神经元经典电路模型的基础上建立介观电路模型。使用经典电路理论和介观量子电路理论,在给予正弦激励下推导神经元细胞膜电压的响应表达式。计算结果表明:神经元细胞膜电压峰-峰值和迟滞回线的面积随激励频率的增大先增大后减小。在经典电路模型中,神经元细胞膜电压峰-峰值和迟滞回线面积达到最大值的频率与外部激励源的幅值有关,而在介观电路模型中,其仅与神经元电路参数有关,不依赖外部激励,更能表征神经元自身的特性。神经元的介观电路模型有益于揭示神经网络的动力学机理,推动脑科学理论体系的发展。By using a cellular membrane capacitor and a potassium ion memristor to characterize the charge storage and memory function of a neuron,this paper modified the classical circuit model and got the mesoscopic circuit model of the Hodgkin-Huxley single ion channel neuron.Based on the classical circuit theory and quantum theory of mesoscopic circuits,the response of membrane voltage of neurons under the sinusoidal excitation was derived.The calculation results show that with the increase in the frequency of the excitation source,the voltage peakpeak value of the membrane of the neuron and its steady-state hysteresis loop area first increase and then decrease.In the classical circuit model,the frequency at which the voltage peak-peak value and the hysteresis loop area reach the maximum depends on the amplitude of the external excitation source,while in the mesoscopic circuit model,it only depends on the circuit parameters of the neuron and is independent of the external excitation,which can better describe the characteristics of neurons.The mesoscopic circuit model of neurons is beneficial to reveal the dynamic mechanism of neural networks and promote the development of brain science theory systems.

关 键 词：Hodgkin-Huxley神经元 介观电路 忆阻器 量子理论 动力学响应 

分 类 号：TM133[电气工程—电工理论与新技术]