本文主要在探討反應-擴散模型組週期解路徑。本文提供一種演算法來求整個解路徑，並延拓隨著一個參數變動的非線性偏微分方程組之週期解，我們稱之為虛擬弧長延拓法。我們將虛擬弧長延拓法應用在反應-擴散模型之非線性偏微方程組上，而週期解路徑之虛擬弧長延拓法是基於打靶法、牛頓法、Crank-Nicolson 法、猜測及解法及隱函數定理等數值方法，且我們將利用其來探討週期解路徑。

The purpose of this paper is to investigate the period solution path of a Reaction-Diffusion Models. This paper will provide the method to calculate whole solution paths and continue the period solution path of partial differential equations which variate a parameter.We call this the pseudo- arclength continuation method. It is applied to the nonlinear elliptic equation of Reaction-Diffusion Models. The main tools of the pseudo-arclength continuation method are shooting method, Newton’s method, Crank-Nicolson’s method, predictor-solver and implicit function theorem. These solutions will be used to confer the period solution paths.

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