更改

In order to characterize voltage-gated channels, the equations are fit to voltage clamp data. For a derivation of the Hodgkin–Huxley equations under voltage-clamp, see.<ref name="JohnstonAndWu">{{cite book|last1=Gray|first1=Daniel Johnston|first2=Samuel Miao-Sin|last2=Wu | name-list-style = vanc |title=Foundations of cellular neurophysiology|year=1997|publisher=MIT Press|location=Cambridge, Massachusetts [u.a.]|isbn=978-0-262-10053-3|edition=3rd}}</ref> Briefly, when the membrane potential is held at a constant value (i.e., voltage-clamp), for each value of the membrane potential the nonlinear gating equations reduce to equations of the form:

In order to characterize voltage-gated channels, the equations are fit to voltage clamp data. For a derivation of the Hodgkin–Huxley equations under voltage-clamp, see.<ref name="JohnstonAndWu">{{cite book|last1=Gray|first1=Daniel Johnston|first2=Samuel Miao-Sin|last2=Wu | name-list-style = vanc |title=Foundations of cellular neurophysiology|year=1997|publisher=MIT Press|location=Cambridge, Massachusetts [u.a.]|isbn=978-0-262-10053-3|edition=3rd}}</ref> Briefly, when the membrane potential is held at a constant value (i.e., voltage-clamp), for each value of the membrane potential the nonlinear gating equations reduce to equations of the form:

为了刻画电压门控通道，'''<font color="#32CD32">该方程拟合自电压钳数据</font>'''。关于电压钳下Hodgkin-Huxley方程的推导，请参阅<ref name="JohnstonAndWu">{{cite book|last1=Gray|first1=Daniel Johnston|first2=Samuel Miao-Sin|last2=Wu | name-list-style = vanc |title=Foundations of cellular neurophysiology|year=1997|publisher=MIT Press|location=Cambridge, Massachusetts [u.a.]|isbn=978-0-262-10053-3|edition=3rd}}</ref>。简单来说，当膜电位保持为一个恒定值（即电压钳取值）时，对于膜电位的每个值，非线性门控方程可以归结为以下形式的方程：

为了刻画电压门控通道，该方程拟合自电压钳数据。关于电压钳下Hodgkin-Huxley方程的推导，请参阅<ref name="JohnstonAndWu">{{cite book|last1=Gray|first1=Daniel Johnston|first2=Samuel Miao-Sin|last2=Wu | name-list-style = vanc |title=Foundations of cellular neurophysiology|year=1997|publisher=MIT Press|location=Cambridge, Massachusetts [u.a.]|isbn=978-0-262-10053-3|edition=3rd}}</ref>。简单来说，当膜电位保持为一个恒定值（即电压钳取值）时，对于膜电位的每个值，非线性门控方程可以归结为以下形式的方程：

: <math>m(t) = m_{0} - [ (m_{0}-m_{\infty})(1 - e^{-t/\tau_m})]\, </math>

: <math>m(t) = m_{0} - [ (m_{0}-m_{\infty})(1 - e^{-t/\tau_m})]\, </math>

While the original experiments treated only sodium and potassium channels, the Hodgkin–Huxley model can also be extended to account for other species of [[ion channel]]s.

While the original experiments treated only sodium and potassium channels, the Hodgkin–Huxley model can also be extended to account for other species of [[ion channel]]s.

虽然最初的实验只处理钠和钾通道，Hodgkin-Huxley模型也可以扩展到其他种类的离子通道。

虽然最初的实验只处理钠和钾通道，Hodgkin-Huxley模型也可以扩展到其他种类的[[离子通道]]。

===漏通道===

===漏通道===

A better [[projection (mathematics)|projection]] can be constructed from a careful analysis of the [[Jacobian matrix and determinant|Jacobian]] of the system, evaluated at the [[equilibrium point]]. Specifically, the [[eigenvalues]] of the Jacobian are indicative of the [[center manifold]]'s existence. Likewise, the [[Eigenvalues and eigenvectors|eigenvectors]] of the Jacobian reveal the center manifold's [[Orientation (geometry)|orientation]]. The Hodgkin–Huxley model has two negative eigenvalues and two complex eigenvalues with slightly positive real parts. The eigenvectors associated with the two negative eigenvalues will reduce to zero as time ''t'' increases. The remaining two complex eigenvectors define the center manifold.  In other words, the 4-dimensional system collapses onto a 2-dimensional plane.  Any solution starting off the center manifold will decay towards the center manifold. Furthermore, the limit cycle is contained on the center manifold.

A better [[projection (mathematics)|projection]] can be constructed from a careful analysis of the [[Jacobian matrix and determinant|Jacobian]] of the system, evaluated at the [[equilibrium point]]. Specifically, the [[eigenvalues]] of the Jacobian are indicative of the [[center manifold]]'s existence. Likewise, the [[Eigenvalues and eigenvectors|eigenvectors]] of the Jacobian reveal the center manifold's [[Orientation (geometry)|orientation]]. The Hodgkin–Huxley model has two negative eigenvalues and two complex eigenvalues with slightly positive real parts. The eigenvectors associated with the two negative eigenvalues will reduce to zero as time ''t'' increases. The remaining two complex eigenvectors define the center manifold.  In other words, the 4-dimensional system collapses onto a 2-dimensional plane.  Any solution starting off the center manifold will decay towards the center manifold. Furthermore, the limit cycle is contained on the center manifold.

在系统的[[平衡点]]处对[[雅可比矩阵]]仔细分析，可以构造出一个更好的[[投影]]。

在系统的[[平衡点]]处对[[雅可比矩阵]]仔细分析，可以构造出一个更好的[[投影]]。具体来说，雅可比矩阵的[[特征值]]指示[[中心流形]]的存在。同样，雅可比的[[特征向量]]揭示了中心流形的[[方向]]。Hodgkin-Huxley 模型有两个负的特征值和两个具有轻微取正的实部的复特征值。随着时间 t 的增加，与两个负特征值相关的特征向量将减少到零。剩下的两个复特征向量定义了中心流形。换句话说，这个四维系统会坍缩到一个二维平面上。<font color = "32CD32">任何开始于中心流形的解将衰减至中心流形。</font>此外，极限环包含在中心流形上。

具体来说，雅可比矩阵的[[特征值]]指示[[中心流形]]的存在。

同样，雅可比的[[特征向量]]揭示了中心流形的[[方向]]。

Hodgkin-Huxley 模型有两个负的特征值和两个具有轻微取正的实部的复特征值。

随着时间 t 的增加，与两个负特征值相关的特征向量将减少到零。

<font color = "32CD32">任何开始于中心流形的解将衰减至中心流形。</font>

此外，极限环包含在中心流形上。

[[File:Hodgkins Huxley Plot.gif|thumb|right|360px|The voltage ''v''(''t'') (in millivolts) of the Hodgkin–Huxley model, graphed over 50 milliseconds. The injected current varies from −5 nanoamps to 12 nanoamps. The graph passes through three stages: an equilibrium stage, a single-spike stage, and a limit cycle stage.

[[File:Hodgkins Huxley Plot.gif|thumb|right|360px|The voltage ''v''(''t'') (in millivolts) of the Hodgkin–Huxley model, graphed over 50 milliseconds. The injected current varies from −5 nanoamps to 12 nanoamps. The graph passes through three stages: an equilibrium stage, a single-spike stage, and a limit cycle stage.

*[[Goldman方程]]

*[[Goldman方程]]

*[[忆阻器]]

*[[忆阻器]]

*[[Neural accommodation]]

*[[神经适应]]

*[[反应-扩散]]

*[[反应-扩散]]

*[[Theta模型]]

*[[Theta模型]]

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