考慮觸媒效應於三自由度系統正平衡點穩定性探討

李中宏(Jung-Hung Li)

指導教授 ： 王國雄

國立中央大學/工學院/機械工程學系/碩士(2006年)

摘要

本論文建構非線性生態平衡模型，藉著模型中三個物種之間的需求與供應關係了解彼此間的競爭和合作對於系統成長與衰退的影響，以及利用觸媒動力學的概念來比較在有觸媒效應的作用之下跟無觸媒效應對於系統成長、衰退有何差異。
同時將非線性系統線性化之後找出系統的平衡點，針對系統設定參數的範圍內，試著了解不同參數之間在何種範圍能找到使系統達到穩定的平衡點。

關鍵字

非線性 ； 生態學模型 ； 觸媒效應 ； 平衡點穩定性

並列摘要

This thesis provides a model for the non-linear ecological system. Depending on the relations between the requirement and the supply for three groups in this model, one can realize the influences of the competition and the cooperation on the development and the recession of the system. With the introducing of the construct of Michaelis-Menten kinetics, the variations of the development or the recession made by the effect of the catalyst can be analyzed.
Furthermore, after transferring the non-linear system to a linear one, the balance situation can be extracted, and one can realize how to adjust the parameters of the system to reach the balance condition in the region which they are assumed accordingly.

並列關鍵字

equilibrium point ； non-linear system ； Michaelis-Menten kinetics

參考文獻

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[2] 祖元剛，趙則海，”非線性生態模型”，科學出版社，2004