本篇論文主要在探討一個非絕熱管狀反應器模型之平衡解路徑上的實分歧點和Hopf分歧點與其分歧解路徑﹒
我們將利用Hopf分歧定理﹑打靶法﹑Rung-Kutta積分公式和牛頓迭代法來求其平衡解路徑上的實分歧點和Hopf分歧點﹐再使用隱函數定理﹑Liapunov-Schmidt降階法﹑切線猜測法﹑割線猜測法和虛擬弧長延拓法﹐來找出過實分歧點和Hopf分歧點的平衡解解分支路徑﹒最後﹐我們將改變其中的參數﹐求得平衡解路徑上的實分歧點和Hopf分歧點與其分歧圖﹒

The thesis investigates real bifurcation points, Hopf bifurcation points and solution branches of steady-state solution paths of a non-adiabatic tubular reactor model.
We use Hopf bifurcation theorem, shooting method, Rung-Kutta integral formula and Newton’s interative method to calculate real bifurcation points and Hopf bifurcation points. We use implicit function theorem, Liapunov-Schmidt reduction method, tangent-predictor method, secant-predictor method and pseudo-arclength continuation method to figure out all solution branches of steady-state solution paths bifurcating from real bifurcation points and Hopf bifurcation points. Finally, we change the parameters to find real bifurcation points, Hopf bifurcation points and bifurcation diagram of the model.

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