三物種之食物鏈模型的動態行為研究

Dynamics of Three Species Food Chain Models with Holling type II Functional Response

潘虹霖(Hung-Lin Pan)

指導教授 ： 楊定揮

淡江大學/理學院/數學學系碩士班/碩士(2013年)

https://doi.org/10.6846/TKU.2013.00549

摘要

本次研究的三個物種食物鏈模型是最簡單的三層食物網類型，一個變數變換後將模型轉化為三個一階常微分方程且有六個參數，起始值為正且有界。然後我們分類邊界平衡點的存在與局部穩定性。並且我們發現一個完整的參數分類，它的必要條件和充分條件存在，但不存在正重根，但正平衡點的局部穩定性數值已驗證。最後我們進行一些數值模擬我們所分類的每個區域。

關鍵字

霍林型二 ； 食物鏈模型 ； 三物種

並列摘要

In this work, the three species food chain models which are the simplest biological models with three trophic levels are investigated. After a non-dimensionless transformation, the model is transformed to a three first order ordinary differential equations with six parameters. The boundedness and positivity of solution with positive initial conditions are first established. Then we classify the existence and local stability of all boundary equilibria. Moreover, we obtain a complete classification of parameter space. For each region of the classification, the necessary and sufficient conditions of existence, non-existence and multiplicity of positive equilibria are obtained. However, the local stability of positive equilibrium is verified numerically. Finally, some numerical simulations are performed for each region of our classification.

並列關鍵字

Holling-type II ； Food Chain Model ； Three Species

參考文獻

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