带有忆阻器的Morris-Lecar神经元模型的放电模式分析和电路实现
Firing Pattern Analysis and Circuit Implementation of Morris-Lecar Neuron Model with Memristor
DOI: 10.12677/OJCS.2020.94009, PDF,  被引量   
作者: 齐国元, 武 宇：天津工业大学电气工程与自动化学院，天津电气工程与能源先进技术重点实验室，天津
关键词: Morris-Lecar神经元系统；忆阻器；电磁感应；ISI分岔；电路设计；Morris-Lecar (M-L) Neuron Model； Memristor； Electromagnetic Induction； ISI Bifurcation； Circuit De-sign
摘要: 根据神经元生物物理环境来完善神经元模型，有助于分析其真实的动力学活动的机理，提高人类对脑活动的认知，在应用上有助于给出正确的神经元信息编码。Morris-Lecar (M-L)是基于离子通道建立的具有代表性的神经元模型，但是该模型未考虑电磁感应效应带来的影响。真实的神经元复杂的离子跨膜运动产生的时变电磁场会影响膜电位。在神经元等效电路中可以用忆阻器来模拟膜电位和电磁感应之间的耦合。本论文选择代表磁通和电荷关系的阈值忆阻器描述细胞膜上电磁感应现象，完善M-L神经元模型，使其更符合人体神经元所处生理环境，提出了一种带有忆阻器的M-L神经元模型。数值模拟证实了不同强度的电磁场可以使神经元的电活动产生明显的膜态跃迁。从峰峰间隔(ISI)角度，利用多参数平面上的ISIs分叉、ISIs放电周期、ISIs方差等研究了带有忆阻器电磁感应的神经元放电模式的转换趋势。最后利用Multisim设计出能够复现神经元生物特性的实用电路，能帮助理解神经元的放电开关机制。
Abstract: Improving neurons and studying their electrical activities according to the real biophysical envi-ronment are of great significance for human cognitive brain activity and neural behavior. Mor-ris-Lecar (M-L) is a representative neuron model based on ion channel, but it does not consider the effect of electromagnetic induction. The complex transmembrane motion of ions on the neuronal cell membrane can establish time-varying electromagnetic fields and affect the transition firing patterns of neurons. In this paper, a threshold memristor is used to describe the electromagnetic induction and magnetic field effects of neuron cell membrane ion exchangeto improve the neuron model, and a memristive Morris-Lecar neuron model is proposed. Numerical simulation confirms that different intensities of electromagnetic fields can produce distinct pattern transition in elec-trical activities of the neuron. From the perspective of neuron’s interspike interval (ISI), the ISIs bi-furcation in the multi-parameter planes, ISIs firing periods, the variance of ISIs and other methods are used to find the trend of the neuron firing pattern transition. Finally, a practical circuit which can reproduce the biological characteristics of neurons is designed by using Multisim, which can help to understand the mechanism of neuronal firing switching.
文章引用：齐国元, 武宇. 带有忆阻器的Morris-Lecar神经元模型的放电模式分析和电路实现[J]. 电路与系统, 2020, 9(4): 61-77. https://doi.org/10.12677/OJCS.2020.94009

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