本論文，旨在探討非線性代數方程組之分歧點與其解分支結構。
首先，我們以隱函數定理為基礎，推導計算出分歧點。由於在分歧點鄰域上具有多重解特性，如何一個一個的找出其解分支，是分歧問題中的重要課題之一。在解決此課題的演算法中，我們除了運用隱函數定理外，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歧點的解分支路徑。
最後，我們將針對三個非線性代數方程組模型，分別求得存在的分歧點及其解分支路徑圖，使我們更清楚知道該系統的分歧現象與定性上的變化。

The main purpose of this thesis is to investigate bifurcation points and solution branches of nonlinear algebraic equations.
First, we use implicit function theorem as the foundation to calculate the bifurcation points. because in the neighborhood of bifurcation point has multiple solutions characteristic ,how to find the solution branches one by one is the important topic of the bifurcation problems. In our algorithm ,in addition to the implicit function theorem, 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 bifurcation points.
Finally, we will investigate three nonlinear algebraic equation models, to get the existence of bifurcation points and solution branches of models, which make us understand the bifurcation phenomenon and the varity of qualitative properties of models more clearly.

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