本文針對氯化鉀離子通道，提出了相關長度為lc 的四階生物離子通道模型, 通
過射擊方法對該模型進行數值模擬。我們的結果分為兩部分, 第一部分我們推導
出具有lc = 0 的二階模型的一維穩態方程，並且氯化鉀離子通道的濃度和電位
函數被完全說明, 第二部分介紹了具有lc ̸= 0 的四階模型的一維穩態方程，用於
描述氯化鉀離子通道的濃度和電位函數的行為和分佈, 第二和第四模型之間的差
異也討論了濃度和電位函數的圖。

In this thesis, the fourth order biological ion channel model with the correlation length $l_c$ is proposed for the KCl channel. This model is numerically simulated via the shooting method. There are two parts for our results. The first part, we derive the one dimensional steady-state equations for the second order model with $l_c=0$, and the concentrations and potential functions are totally illustrated for the KCl channel. The second part, the one dimensional steady-state equations for the fourth order model with $l_c \ne 0$ is also presented for describing the behaviors and profiles of the concentrations and potential functions for the KCl channel. The difference between the second and the fourth model are also discussed for the graph of the concentrations and potential functions.

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