三自由度系統正平衡點穩定性探討

陳彥均(Yen-Chun Chen)

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

本文主要是依據生態學裡的族群動態，運用Logistic和Lotka-Volterra’模型，以及Peter Yodzis、Kevin McCann、Alan Hastings和Gary R.Huxel學者文章的模型，創造出三自由度的生態非線性系統模型，並研究了解各參數對此模型的影響與討論其現象。
文中還將方程式簡化，形成ㄧ特殊例子，並對此例子做正平衡點的穩定性討論。首先將平衡點分類為四種主要類型，平衡點全為零、平衡點二項為零，平衡點ㄧ項為零，平衡點全不為零，利用羅斯穩定準則(Routh Stability Criterion)來判斷其穩定度，分析其穩定的邊界。

關鍵字

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並列摘要

The current study is mainly based on the ethnicity trends in ecology. It is used the Logistic, Lotka-Volterra models, and several scholars’ food-web models, such as Peter Yodzis, Kevin McCann, Alan Hastings and Gary R.Huxel, to create the three degree of freedom non-linear systematic model of ecology. Furthermore, the study is also analyzed and discussed the influence of every parameter on the model.
In the research, the stability of the positive equilibrium point of the special example which is formed by simplifying the equation is discussed. First, the equilibrium point is categorized into four kinds of main types that is all equilibrium points are zero , two equilibrium points are zero, one equilibrium point is zero, and the whole equilibrium point is not zero. Then, utilizing Routh Stability Criterion to judge its steady degree and analyze its steady border.

並列關鍵字

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參考文獻

[9] Kevin McCann,Alan Hastings,Gary R.Huxel,”Weak trophic interactions and the balance of nature”,NATURE,Vol.395,Oct. 22,1998.

[10] Peter Yodzis,”diffuse effect in food webs ecology”,

rporating mathematical biology in lower-level math

courses”.

[13] J.D.Murray,”Mathematical Biology”.