April 2014
Beginner to intermediate
830 pages
15h 21m
Chinese
Content preview from Mathematica 錦囊妙計
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518
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第十三章
13.5 掠食者與獵物模型的動力學模擬
問題點
你想要模擬掠食者與獵物模型，觀察掠食者與獵物的數量如何隨時間演變。[Page-519]
ch13.indd 518 2014/4/2 下午 02:31:01
13.5 掠食者與獵物模型的動力學模擬
|
519
解決方案
假設模型中的掠食者為狐狸，獵物為野兔，
G
代表野兔的成長率，
K
代表環境的負荷量，
則野兔的數量
R
與狐狸的數量
F
可使用差分方程式模擬。至於方程式的形式與常數的意
義詳見後文「討論說明」部分。
若初始條件給定，
NestList
指令是運算此動力學模型的方法之一。[Page-520]
上圖呈現模擬的結果。在一開始，狐狸的數量緩慢地隨著野兔的數量增加，直到出現一
個反折點，由於狐狸過多導致野兔的數量開始減少，如此反覆循環，最終此模型將演化
至一穩定狀態。
討論說明
獵物方程式假設成長數量與目前數量成正比，但需受限於 logistic 模型，這是因為環境
負荷量是有限的，此外還須減去一項正比於掠食者與獵物乘積的數目，這是受掠食者捕
食的數量，其常數 0.0001 代表掠食者捕食的效率。而掠食者方程式則假設成長數量與捕
食獵物的能力成正比（與獵物方程式有相同的項），並減去自然死亡的數量（上例的死
亡率為百分之二）。
ch13.indd 519 2014/4/2 ...
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