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M电流诱导的博格达诺夫-塔肯斯分岔与神经元兴奋性类别的转换

M-current induced Bogdanov-Takens bifurcation and switching of neuron excitability class.

作者信息

Al-Darabsah Isam, Campbell Sue Ann

机构信息

Department of Applied Mathematics and Centre for Theoretical Neuroscience, University of Waterloo, N2L 3G1, Waterloo, ON, Canada.

出版信息

J Math Neurosci. 2021 Feb 15;11(1):5. doi: 10.1186/s13408-021-00103-5.

DOI:10.1186/s13408-021-00103-5
PMID:33587210
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7884550/
Abstract

In this work, we consider a general conductance-based neuron model with the inclusion of the acetycholine sensitive, M-current. We study bifurcations in the parameter space consisting of the applied current [Formula: see text], the maximal conductance of the M-current [Formula: see text] and the conductance of the leak current [Formula: see text]. We give precise conditions for the model that ensure the existence of a Bogdanov-Takens (BT) point and show that such a point can occur by varying [Formula: see text] and [Formula: see text]. We discuss the case when the BT point becomes a Bogdanov-Takens-cusp (BTC) point and show that such a point can occur in the three-dimensional parameter space. The results of the bifurcation analysis are applied to different neuronal models and are verified and supplemented by numerical bifurcation diagrams generated using the package MATCONT. We conclude that there is a transition in the neuronal excitability type organised by the BT point and the neuron switches from Class-I to Class-II as conductance of the M-current increases.

摘要

在这项工作中，我们考虑一个包含乙酰胆碱敏感的M电流的基于电导的通用神经元模型。我们研究了由施加电流[公式：见原文]、M电流的最大电导[公式：见原文]和泄漏电流的电导[公式：见原文]组成的参数空间中的分岔情况。我们给出了确保存在Bogdanov-Takens（BT）点的模型的精确条件，并表明通过改变[公式：见原文]和[公式：见原文]可以出现这样一个点。我们讨论了BT点变为Bogdanov-Takens-尖点（BTC）点的情况，并表明这样一个点可以出现在三维参数空间中。分岔分析的结果应用于不同的神经元模型，并通过使用MATCONT软件包生成的数值分岔图进行验证和补充。我们得出结论，由BT点组织的神经元兴奋性类型存在转变，并且随着M电流的电导增加，神经元从I类转变为II类。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6f1e/7884550/1a2a595e36d2/13408_2021_103_Fig14_HTML.jpg
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