论文标题
M电流诱导的Bogdanov-Takens分叉和神经元兴奋性类的转换
M-current Induced Bogdanov-Takens Bifurcation and Switching of Neuron Excitability Class
论文作者
论文摘要
在这项工作中，我们考虑了一个基于通用电导的神经元模型，其中包含乙胆碱敏感的M-电流。我们在参数空间中研究分叉，由应用电流组成，$ i_ {app} $ M-电流的最大电导率，$ g_m $，以及泄漏电流的电导率，$ g_l $。我们为模型提供了确切的条件，以确保存在bogdanov-takens（BT）点，并通过改变$ i_ {app} $和$ g_ {m} $来显示这样的点。当BT点成为Bogdanov-Takens-Cusp（BTC）点并表明在三维参数空间中可能发生这种点时，我们将讨论案例。分叉分析的结果应用于不同的神经元模型，并通过使用软件包矩阵生成的数值分叉图进行了验证和补充。我们得出的结论是，随着M-电流增加的电导率，BT点组织的神经元兴奋性类型和神经元从I类转换为II的过渡。
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, $I_{app}$ the maximal conductance of the M-current, $g_M$, and the conductance of the leak current, $g_L$. We give precise conditions for the model that ensure the existence of a Bogdanov-Takens (BT) point and show such a point can occur by varying $I_{app}$ and $g_{M}$. 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 organized by the BT point and the neuron switches from Class-I to Class-II as conductance of the M-current increases.
