Firing patterns of the modified Hodgkin-Huxley models subject to Taylor's formula
Firing patterns of the modified Hodgkin-Huxley models subject to Taylor's formula
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根据泰勒公式修改后的霍奇金赫胥黎模型的射击模式
DOI：
10.1016/j.physa.2020.124405
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发表时间：
2020
影响因子：
3.3
通讯作者：
Zhang Xiaohan
中科院分区：
文献类型：
--
作者：
Liu Yaru;Liu Shenquan;Zhan Feibiao;Zhang Xiaohan
众所周知，经典的Hodgkin-Huxley(HH)方程具有复杂的非线性动力学性质。本文研究了28个修正的HH模型的离子电导方程，计算了离子通道电导，并模拟了神经元的放电模式。有趣的是，发现并证实了离子电导正是泰勒公式原点的四级项的系数。结果表明，这些模型的方程与原点附近电导的二变量Taylor公式关于通道参数密切相关。我们非常详细地考虑了一个具体的模型作为例子。我们发现，电导曲线一般都是相同的，但电导峰不同。在改进的HH模型中观察到了几种激发模式，包括猝发和混合模式振荡。混合模式振荡的出现可能对今后的工作特别有意义。(C)2020爱思唯尔B.V.保留所有权利。
It is well known that the classical Hodgkin-Huxley (HH) equations exhibit complex nonlinear dynamic properties. This paper examines the ion conductance equations of 28 modified HH models, calculating the ion channel conductance and simulating neuronal firing patterns. It is interesting to discover and confirm that the ion conductance is exactly the coefficient of the fourth-order term at the origin of Taylor's formula. It is demonstrated that the equations for these models are closely related to the two-variable Taylor's formula of the conductance around the origin in terms of the channel parameters. We consider one specific model in great detail as an example. We find that the conductance curves are generally of the same form, but that the conductance peaks differ. Several firing patterns are observed in the modified HH models, including bursting and mixed-mode oscillations. The emergence of mixed-mode oscillations in particular may be of interest for future work. (C) 2020 Elsevier B.V. All rights reserved.