在本篇論文中，我們將探討Brusselator模型解路徑之延拓。我們運用有限差商法將模型離散，以及利用數值分析的方法，求得數學模型的轉彎點與正則點，並延拓出其整個解路徑，以探討模型的多重解的存在，有助於我們了解Brusselator模型方程在定性上的變化。本文中，我們使用隱函數定理、有限差分法、牛頓迭代法、割線預測法及虛擬弧長延拓法來找出我們Brusselator模型在有限邊界內之解路徑，並在解路徑中找出其轉彎點與正則點，運用適當的迭代法來分析並探討Brusselator模型解路徑的變化。

In this thesis, we will investigate the continuation of solution paths for the Brusselator model. We ues the central difference method to investigate the multiple solution paths of the Brusselator model. Moreover, we investigate a Brusselator model to find solution paths containing bifurcation points, turning points and regular points of the Brusselator model. It will be helpful to understand the qualitative properties in the solutions of the Brusselator model.
In this paper, we apply implicit function theorem, central difference method, Newton’s iterative method, secant predictor method, pseudo–arclength continuation method to find the solution paths of the Brusselator model. At the same time, we use numerical methods to find solution paths containing bifurcation points, turning points and regular points and use proper iterative methods to analysis and investigate the continuation of solution paths for the Brusselator model.

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