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研究生:陳光鴻
研究生(外文):Kuan-Hung Chen
論文名稱:生態數學模型的動態行為
論文名稱(外文):On the Lotka-Volterra dynamics
指導教授:陳兆年
指導教授(外文):Chao-Nien Chen
學位類別:碩士
校院名稱:國立彰化師範大學
系所名稱:數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:35
中文關鍵詞:生態數學模型Hopf分歧周期解擴散性
外文關鍵詞:Lotka-Volterra competition modelHopf bifurcationperiodic solutionMatlabreaction-diffusion systemdiffusion
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本論文之主旨在嘗試了解Lotka-Volterra模型中,三個物種之間生態競爭的動態行為與過程.此模型之特性是在生態上相互剋制;即三個物種中若其中之一消失,則在兩兩競爭之下,第一個物種將淘汰第三個物種,第二個物種將淘汰第二個物種,第二個物種將淘汰第一個物種.利用Hopf分歧理論以及藉助數學軟體Matlab做數值分析,我們找出許多不同的周期解,其中包括擴散性對此系統周期解的影響.

The aim of this thesis is to study the dynamics of Lotka-Volterra competition model with three species. This model cooresponds to the biological circumstance where in purely pirwise competition 1 beats 3, 3 beats 2 and 2 beats 1. With the aid of Hopf bifurcation, we found various periodic solutions numerically by making use of Matlab. Furthermore, diffusion on such systems has also been investigated.

1. Introduction........................................1
2. A Hopf bifurcation result...........................9
3. Numerical study on periodic solutions..............23
4. Diffusion influence................................27
5. Reference..........................................34

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