一类四维神经元模型的放电模式研究
Study on Firing Patterns for a Four-Dimensional Neuron Model
DOI: 10.12677/DSC.2017.64023, PDF, HTML, XML, 下载: 1,784  浏览: 3,153  国家自然科学基金支持
作者: 刘火霞, 刘宣亮：华南理工大学数学学院，广东 广州
关键词: 四维神经元模型；快慢动力学；分岔；簇放电；Four-Dimensional Neuron Model； Fast-Slow Dynamics； Bifurcation； Bursting
摘要: 本文研究一类描述坐骨神经慢性压迫性损伤的四维神经元模型。利用快慢动力学方法，并结合数值模拟结果来分析此模型的各种放电模式。通过作出快子系统随慢变量变化的单参数分岔图，以及对相应于放电状态的稳定极限环的讨论，来得到不同放电模式出现的动力学机制。
Abstract: This paper studies a sciatic nerve chronic constriction injury model. This model consists of four coupled nonlinear differential equations. By using the fast-slow dynamical methods and numerical simulations, we analyze the firing patterns of the model. We give the single parameter bifurcation diagrams of the fast subsystem, and discuss the stable limit cycles which are corresponding to the firing state of the neuron. Dynamical mechanisms of different firing patterns are obtained.
文章引用：刘火霞, 刘宣亮. 一类四维神经元模型的放电模式研究[J]. 动力系统与控制, 2017, 6(4): 180-186. https://doi.org/10.12677/DSC.2017.64023

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