本篇論文主要在探討隨著參數變動的非線性常微分方程組之數學模型。在解此模型的穩定解時，將產生非線性方程組。本文提供一演算法來求並延拓隨著一個參數變動的非線性常微分方程組之週期解，我們稱他為擬弧長演算法（pseudoarclength algorithm），擬弧長演算法係基於打靶法（shooting method）、隱函數定理（implict function theorem）、猜測及解法（predictor-solver）以及本文裡所提到的延著解路徑延拓的方法。運用虛擬弧長延拓法可以使解路徑順利通過轉彎點或是跳過分歧點,而能延拓出整個解路徑來。從數值實驗的結果，我們成功的得到常微分方程組的多重週期解與單一解的區間性及穩定性，我們發現初始值對振幅具有決定性的影響。

In this paper, we discussed the mathematical models in the form of systems of nonlinear ordinary differential equations depending on a chosen physical parameter. Stationary solutions of the models then result from a set of nonlinear ( algebraic) equations.
An algorithm for continuation of periodic solutions in ordinary differential equations in dependence on a parameter is presented in this article which we called it as pseudoarclength algorithm. The pseudoarclength algorithm for the continuation of periodic solutions based on the shooting method, implicit function theorem, predictor-solver method and continuation along the arc-length of solutions path is described in this paper.
The pseudoarclength algorithm can pass through limits points or jump over bifurcation points so that we can find out the whole solutions path. From the numerical experiment, we trace out the range between multiple periodic solutions and single solutions of ordinary differential equations. Finally, we find that the initial value has significant influence on the amplitude .

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