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研究生:歐岳良
研究生(外文):Yuei-Liang Ou
論文名稱:時滯對捕食模型之局部穩定性的影響
論文名稱(外文):The Influence of Time Delay on Local Stability for a Predator-Prey System
指導教授:何肇寶何肇寶引用關係
指導教授(外文):Chao-Pao Ho
學位類別:碩士
校院名稱:東海大學
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:1999
畢業學年度:87
語文別:英文
論文頁數:30
中文關鍵詞:時滯捕食系統
外文關鍵詞:Time DelayPredator-Prey System
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本篇論文主要探討具有時滯之捕食模型的動態行為。
首先,我們將探討下列的捕食系統之局部穩定性,
\ dot{x_1}(t)=rx_1(t)[1-\frac{x_1(t)}{K}]-mx_1(t)x_2(t)
\ dot{x_2}(t)=-dx_2(t)+cx_1(t)x_2(t)
其中x_1及x_2分別表被捕食者及捕食者的族群量;且r, K, m, d, c
為正的常數。進而討論時滯參數對此捕食模型之局部穩定性的影響。最後,我們將用實例來說明其結果。

The aim of the thesis is to study the dynamical behavior of a predator-prey system with time delay.
Consider the following predator-prey system
\dot{x_1}(t)=rx_1(t)[1-\frac{x_1(t)}{K}]-mx_1(t)x_2(t)
\dot{x_2}(t)=-dx_2(t)+cx_1(t)x_2(t)
where x_1 and x_2 are density of prey and predator, respectively, and r, K, m, d, c are positive constants.
We first discuss its local stability. Then we study the change of the local stability for the predator-prey system with a single
delay. Finally, we conclude with an example.

1 Introduction 2
2 Preliminaries 4
3 The Model without Delays 12
4 The Model with a Single Delay 17
5 Examples 24
6 Conclusion 28

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