由於生物廢棄物的處理技術相當重要，故最近幾年來微生物的混合培養技術深受大家的重視，本研究實施菌類－基質(Cell-Substrate)和被捕食者－捕食者(Prey-Predator)相互作用之生化反應在兩個生化反應槽串聯之穩定狀態和動態分析，對於菌類－基質之生化反應，若以Monod模式來表示菌類之比生長速率，則此兩個生化反應槽串聯之反應系統共有三種型態之穩定狀態，本研究對此三種型態之穩定狀態和穩定度作深入的分析，對於此反應系統之動態行為，則由電腦運用數值分析的方法及電腦繪圖進行分析工作，動態分析的結果顯示此生化反應系統之動態行為，以穩定之穩態(Stable Steady State)為主。
對於被捕食者－捕食者相互作用之生化反應，此系統方程式係假設完全混合為前提所導出者，並假設被捕食者(細菌類)僅以培養系中之可溶性成分[基質(葡萄糖類)]為食物，而捕食者(纖毛蟲類)僅以被捕食者為食物來增殖，與環境之間並無可溶性物質之進出。若以Monod模式來表示被捕食者和捕食者之比生長速率，則此兩個生化反應槽串聯之反應系統共有六種型態之穩定狀態，本研究對此六種型態之穩定狀態和穩定度作深入的分析。對於動態分析，本研究運用數值分析的方法來求解系統之動態方程式，並運用電腦繪圖來進行動態分析，動態分析的結果顯示此生化反應系統之動態行為可為穩定之穩態(Stable Steady State)或循環振盪(Limit Cycle)。

Because the techniques of the biochemical waste treatment are very important, the techniques of the cultivation of the microorganism have received more attention in recent years. A study is conducted to analyze the steady states and dynamic bechavior of the reactions of the cell-substrate and the prey-predator interaction in two chemostats in series. For the reaction of cell-substrate in two chemostats in series, if the specific growth rate of the Monod model is used for the cell , there are three types of steady states for this reaction system. These three types of steady states and stability are analyzed in detail. The dynamic behavior of this reaction system is analyzed by the numerical method and computer graphs. The results show that the dynamic behavior of this system consists of stable steady states.
For the prey-predator interaction, the dynamic equations are derived by assuming that the reaction is occurring in a perfectly mixed condition. It is assumed that the prey( such as the bacterium ) is only fed with the substrate(such as the glucose) and the predator(such as the ciliate ) is only fed with the prey and no other substance exchanges between the system and the environment. If the Monod model is used for the specific growth rate of both the prey and the predator, there are six types of steady states for this reaction system and the six types of steady states and stability are analyzed in detail. The dynamic equations of this system are solved by the numerical method and the dynamic analysis is performed by computer graphs. The results show that the dynamic behavior of this system consists of stable steady states and limit cycles.

摘要...………………………………………………………………………………..…..iv
英文摘要..……………………………………………………………………….……….v
誌謝....….……………………………………………………………………………….. vi
目次....….…………………………………………………………………………...….. vii
表目錄....……………………………………………………………….…...….……….. ix
圖目錄..……………………………………………………………….………….………x第一章 前言...………………………………………………………………………......1
1.1 研究背景及目的……….……………………………………………….….….1
1.2 研究方法………………………………………………………………...….…2
1.3 預期完成之工作項目及成果………………………………………..………..3
第二章 菌類－基質在兩個生化反應槽串聯之穩定狀態和動態分析…………..…….4
2.1 動態系統方程式..………………………………………………………..……4
2.2 穩定狀態..………………………………………………………………..……6
2.3 穩定度分析……………………………………………………………....……7
2.4 動態分析…………………………………………………..…………………15
2.5 討論………………………………………………………..………….……...29
第三章 被捕食者－捕食者在兩個生化反應槽串聯之穩定狀態和動態分析…….…30
3.1 動態系統方程式…………………………………………..…………….…...30
3.2 穩定狀態…………………………………………………..………….……...32
3.3 穩定度分析………………………………………………..……….………...39
3.4 動態分析…………………………………………………..…….…………...58
3.5 討論………………………………………………………..………………..153
第四章 結論………………………………………………………………….…….….155
參考文獻…….……………………………………………………………...…...……..158
附錄A 計算機程式計算菌類-基質在兩個生化反應槽串聯之第一個生化反應
槽之動態…………………………………………………………….………161
附錄B 計算機程式計算菌類-基質在兩個生化反應槽串聯之第二個生化反應
槽之動態……………………………………………………………….……163
附錄C 計算機程式計算菌類-基質在兩個生化反應槽串聯之穩定狀態…….…..165
附錄D 計算機程式計算菌類-基質在兩個生化反應槽串聯之特徵值……….…..166
附錄E 計算機程式計算被捕食者－捕食者在兩個生化反應槽串聯之第一個
生化反應槽之動態……………………………………………………….…167
附錄F 計算機程式計算被捕食者－捕食者在兩個生化反應槽串聯之第二個生化
反應槽之動態……………………………………………………….………170
附錄G 計算機程式計算被捕食者－捕食者在兩個生化反應槽串聯之第一、二、
三型態之穩定狀態………………………………………………………….173
附錄H 計算機程式計算被捕食者－捕食者在兩個生化反應槽串聯之第四型態之
穩定狀態…………………………………………………………………….174
附錄I 計算機程式計算被捕食者－捕食者在兩個生化反應槽串聯之第五型態之
穩定狀態…………………………………………………………………….176
附錄J 計算機程式計算被捕食者－捕食者在兩個生化反應槽串聯之第六型態
之穩定狀態……………………...…………………………………………..177
附錄K 計算機程式計算被捕食者－捕食者在兩個生化反應槽串聯之特徵值…………………………………………………………………………….179
附錄L 菌類-基質在兩個生化反應槽串聯之質量平衡………………………...….181
附錄M 被捕食者－捕食者在兩個生化反應槽串聯之質量平衡……………….…183

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