兩族群競爭與共存之整合及K戰略之應用

A Hybrid 2D-Model from Competition and Coexistence Models and Applications of K-Strategists

古宏麒(Hong-chi Ku)

指導教授 ： 莊陸翰

大同大學/電機資訊學院/應用數學學系所/碩士(2008年)

摘要

生物族群間的互動關係在很久以前就已被學者應用數學工具來描述成數學模型，如Lotka與Volterra提出的兩族群競爭模型。
在此篇論文當中，我們將兩族群間競爭關係及互利共生關係的數學模型整合成一個通用的數學模型。此模型是由兩個非線性微分方程式以及六個參數所構成的一個系統；這些參數意義代表著兩族群的自然出生率、環境負荷量以及相互影響個體之效應。在兩族群之環境負荷量相等及兩族群相互影響個體之效應相等的參數條件下，我們分析兩族群之間的互動關係為何及數值模擬來觀察其狀態軌跡的行為。並從中發現僅憑檢視系統之非零平衡態在座標平面上的位置，就可判定兩族群的互動是競爭或是互利共生的關係。此外，又探討一種被稱為環境負荷量戰略(K-strategist)的操控族群技巧，它藉由某族群的環境負荷量，來改變兩族群之間的互動關係可使優劣勢互換。
此整合之數學模型，不僅可用於探討生物族群的互動，也可應用於政黨間或是公司企業間的互動…等，來評估衡量之間的利益關係。

關鍵字

環境負荷量 ； 互利共生 ； 競爭

並列摘要

The academic had described the interaction between ethnic groups and the mathematical model by mathematical tools for a long time. For example, Lotka and Volterra established the 2D competition model.
In this paper, we simplified the mathematical model of competition and mutualism of two groups to a generalized model. It formed a system with two nonlinear differential equations and six parameters. These parameters represented two groups’ natural birth rate, carrying capacity, interactive effect. Under the carrying capacity equal and the interactive effect equal, we analyzed the interactions of two groups and observed their behaviors by numerical simulation. From the inside of the position of the nonzero equilibrium of the system, we could determine what the interaction was. Additionally, a group’s controlling skill which was called K-strategist, could further change the two groups’ advantage and inferiority.
The simplified model not only treats the interaction between ethnic groups but also applied to political parties or to businesses to measure the benefit.

並列關鍵字

competition ； carrying capacity ； mutualism

參考文獻

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