PARTITION OF THE HODGKIN-HUXLEY TYPE MODEL PARAMETER SPACE INTO THE REGIONS OF QUALITATIVELY DIFFERENT SOLUTIONS
PARTITION OF THE HODGKIN-HUXLEY TYPE MODEL PARAMETER SPACE INTO THE REGIONS OF QUALITATIVELY DIFFERENT SOLUTIONS
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DOI：
10.1007/bf00197721
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发表时间：
1992-03-01
影响因子：
1.9
通讯作者：
DICK, OE
中科院分区：
文献类型：
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作者：
BEDROV, YA;AKOEV, GN;DICK, OE
我们研究了Hodgkin-Huxley系统稳定解的类型、其参数的取值与恒定外加电流(I)之间的关系。选取最大Na~+(g(Na)bar)、K~+(g(K)bar)电导和电压位移(Gm、Gh、Gn)作为系统的可变参数。要解决这个问题，只需找到属于边界的点，将系统的参数空间划分为定性不同类型的稳定解(稳定状态和稳定周期振荡)的区域即可。几乎在整个I的生理范围内，一种稳定的溶液是由稳定状态的类型(稳定或不稳定)决定的。利用这一事实，可以通过分析线性化系统的雅可比矩阵的特征值谱来获得该问题的近似解。在三参数空间(I，g(NA)bar，g(K)bar)，(I，Gm，Gh)，(I，Gm，Gn)中构造了边界平面截面族。
We have examined the problem of obtaining relationships between the type of stable solutions of the Hodgkin-Huxley type system, the values of its parameters and a constant applied current (I). As variable parameters of the system the maximal Na+ (g(Na)BAR), K+(g(k)BAR) conductances and shifts (Gm, Gh, Gn) of the voltage-dependences have been chosen. To solve this problem it is sufficient to find points belonging to the boundary, partitioning the parameter space of the system into the regions of the qualitatively different types of stable solutions (steady states and stable periodic oscillations). Almost all over the physiological range of I, a type of stable solution is determined by the type of steady state (stable or unstable). Using this fact, the approximate solution of this problem could be obtained by analyzing the spectrum of eigenvalues of the Jacobian matrix for the linearized system. The families of the plane sections of the boundary have been constructed in the three-parameter spaces (I,g(NA)BAR, g(K)BAR), (I, Gm, Gh), (I, Gm, Gn).