細胞代謝中，物質發生自身催化的現象是不可避免的，細胞掠取食物或其它來源進而轉成所需之能量，而其過程中需經過複雜且大量的自身催化反應，其中最簡單且運用最廣泛的系統就是醣的分解過程了。
此代謝過程是細胞經過無氧過程，將葡萄糖分解而生成能量三磷酸腺苷(ATP)，而某些自身催化結構因含有相似的自催化過程，因此將導致不穩定性發生，所以須特別加以控制。
在本論文中，吾人將研究自身催化的代謝路徑，了解葡萄糖分解過程，並建立醣酵解方程式，而吾人將利用非線性分析的方式，更完整來分析此方程式。在過程中發現，系統存在有極限圓的現象，而吾人將求得參數影響度係數來比較其參數的影響性，接著經由合理的參數來建立嚴密的穩定邊界，最後討論參數對應之酵素的影響性。

Autocatalytic pathway is a necessary part of core metabolism. In every cell, food and resources are broken down to produce energy and components via processes that also require the use of those same components and energy. Indeed at a certain level all biological networks are complex and massively autocatalytic. The simplest and most widely studied autocatalytic network is the glycolytic pathway.
This metabolic pathway is used by the cell to produce energy adenosine triphosphate (ATP) anaerobically by breaking down glucose. Its special autocatalytic structure, like the structure of many similar autocatalytic networks, can lead to instabilities and makes it particularly hard to control.
In this thesis, I study autocatalytic metabolic networks, and specifically glycolysis, to investigate fundamental performance tradeoffs in these network topologies.I will use nonlinear analysis method to analyze a nonlinear model for glycolysis.Limit cycle oscillation is found in this nonlinear model. Several parameters affecting the amplitude and frequency of the limit cycle are compared by a quantitative method. Finally, I establish tight stability bounds for the feedback gains involved in the glycolysis.

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