臺灣博碩士論文加值系統

本論文主要在探討一個具外來週期作用力的化學混合反應器模型之週期倍增分歧問題的分歧點、週期解解分支及倍週期解解分支結構.
首先,我們利用打靶法及牛頓迭代法,來推導計算出週期倍增分歧點.並以隱函數定理為基礎,運用Liapunov-schmidt降階法,虛擬弧長延拓法,割線猜測法及牛頓迭代法等數值方法,來延拓出所有通過週期倍增分歧點的解分支路徑.
最後,我們改變其中某一參數,而將其他參數固定,分別求得分歧現象與分歧點的變化.

The main purpose of this thesis is to investigate the bifurcation points , periodic solution branches and periodic-doubling solution branches of a well-mixed reactor with the Brusselator chemical reaction and external periodic forcing model .
First, we use shooting method and newton’s interative method to calculate the periodic-doubling bifurcation points .We use implicit function theorem as the foundation to quote the numerical method of the Liapunov-Schmidt reduction method, pseudo-archength continuation method, secant-predictor method, and Newton’s interative method,to continue all solution branches from periodic-doubling bifurcation points.
Finally, we change one of the parameters and fix the others to find the bifurcation phenomenon and the changes of bifurcation points .

第一章 緒論 1
第二章 分歧理論與虛擬弧長延拓法 4
2.1 分歧問題 ……………………………………………………… 4
2.2 隱函數定理與分歧理論 ……………………………………… 6
2.3 局部延拓法 …………………………………………………… 8
2.4 虛擬弧長延拓法 …………………………………………… 11
第三章 常微分方程週期倍增分歧問題的數值解法 13
3.1 週期倍增分歧點之求法……………………………………… 13
3.2 選取過週期倍增分歧點的週期解解分支延拓方向………… 28
3.3 週期解解分支的延拓………………………………………… 37
3.4 過週期倍增分歧點的倍週期解分支延拓方向與路徑……… 41
3.5 演算法………………………………………………………… 42
第四章 數值實驗 48
4.1 實驗4.1…………………………………………………… 50
4.2 實驗4.2…………………………………………………… 101
4.3 實驗4.3…………………………………………………… 120
第五章 結論 130
參考文獻 132

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