臺灣博碩士論文加值系統

本篇論文主要是探討兩個平行食物鏈之數學分析。其系統狀態為兩個同一物種的被捕食者（Prey）共同競爭有限的資源，捕食者（Predator）亦為兩個同一的物種，且被補食者與補食者各自具有不同的死亡率。我們由簡而繁的討論食物鏈由不同元素組成時的結果。

首先我們關心各種較基本食物鏈系統的結論。在第三章我們考慮單一食物鏈的情形，其方法與結論相似於參考書目[10]所示。第四章是探討兩平行食物鏈完全缺乏捕食者與只有一條食物鏈具有捕食者的情況，當兩平行食物鏈皆無捕食者時，結果有兩種：所有物種都消失；或者兩個被捕食的物種趨於一個平衡點，且其數量的總和為一定值；當只有一條食物鏈具有捕食者時，則此捕食者會隨著時間滅絕，此時系統的結果如同完全缺乏捕食者的情況。

接下來第五章探討主題兩平行食物鏈的情形，依其參數與初始條件的不同可得到以下四種不同的結果：所有的物種皆消亡；只有被捕食者的物種存在，且其總和為一定值；所有被捕食者與捕食者共存於一個穩定的平衡點狀態；所有被捕食者與捕食者共存於一個互有消長的來回振盪狀態。在本章我們對於前三種結果給予了數學上的分析證明，但對第四種情況我們只有數值上的模擬結果，在第六章中可見其圖形。

The object of this paper is to study the two parallel food chains model. We show that the dynamic outcomes of this model are sensitive to parameter values and initial data. There are several possible outcomes as follows: 1) Both predator and prey go extinct; 2) only the prey species survive; 3) predator and prey coexist in the form of equilibrium;4) predator and prey coexist in the form of oscillation. We analyze the case (1) ~ (3) rigorously. For the case (4), we do numerical simulations to describe all possible phenomena.

1.Introduction.............................................1
2.The model of two parallel food chains....................2
3.Preliminary results of a single food chain model ........4
4.Two parallel food chains with either no predators or only one predator..............................................12
5.Mathematical analysis of two parallel food chains system....................................................16
5-1 Rest point and their local stability..................16
5-2 Global analysis of the two parallel food chains.......24
6.Discussion..............................................30
References................................................35

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