本論文主要是由Hopf 分歧理論, 配合牛頓迭代法來求得雙聯優非線性微分方程組的分歧點(包含實數分歧點及Hopf 分歧點). 續由隱函數定理、Liapunov -Schmidt降階法、割線猜測法及虛擬弧長延拓法來得到通過實分歧點及Hopf分歧點平衡解路徑.
此外, 我們也由打靶法、隱函數定理、Liapunov-Schmidt降階法、割線猜測法及虛擬弧長延拓法並配合Rung-Kutta積分法來得到該方程組通過Hopf 分歧點之週期解路徑.

In this thesis﹐we use the Hopf bifurcation theorem with Newton’s interactive method to find the bifurcation points (include real bifurcation points and Hopf bifurcation points) of the non-linear interconnected differential equation’s set. And then use the implicit function theorem, Liapunov-Schmidt reduction method, secant-predictor method and pseudo-arclength continuation method, to obtain the steady-state solution paths passing through real bifurcation points and Hopf bifurcation points.
We also use the shooting method, implicit function theorem, Liapunov-Schmidt reduction method, secant-predictor method and pseudo-arclength continuation method, with Runge-Kutta method to find the periodic solution paths bifurcating from the Hopf bifurcation.

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