本論文,旨在探討非線性邊界值微分方程組之分支點及多重解路徑.
首先,我們以隱函數定理為基礎,推導計算出分支點,並引用有限維度Liapunov-Schmidt降階法、解分支方向、割線預測法、牛頓迭代法以及虛擬弧長延拓法等數值方法來延拓出所有通過分支點的解分支路徑.
最後,我們並分別選擇特定的變數作為參數,利用一個非線性邊界值微分方程組模型求得存在的分支點及多重解路徑,使我們更清楚了解該系統的分歧現象與定性上的變化.

The main purpose of this thesis is to investigate branch points and multiple solutions of nonlinear boundary-valued differential equations.First,we use implicit function theorem as the foundation to calculate the branch points.We also quote the numerical method of finite dimensional Liapunov-Schmidt reduction method,the direction solution branch,secant predictor method,Newton’s interative method,and pseudo–arclength continuation method,to continue all solution branches and pass through branch points.
To solve the existed branch points and solution paths of the model,we also investigate the solution structure of the model by choosing a specific variable as the parameter.The results help us to understand the bifurcation phenomenon and the variety of qualitative properties of the model.

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