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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