兩掠食者-一被掠食者食物網模型的動態行為研究

Dynamics of Two-Predators-One-Prey Food Web Models with Holling-type II Functional Response

林佩萱(Pei-Hsuan Lin)

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.2013.00556

摘要

我們選了一個 Holling Type II 的兩個掠食者一個被掠食的動態模型，
討論這模型在二維的平衡點穩定性、邊界的穩定性、局部的穩定性和唯一性，
接著是在三維的情況下，邊界平衡點的局部分析。另外，還探討了這模型在
Global 的動態情況是否會有出現共存的可能。最後經過數據的分析，我們可
以知道我們的模型是不會出現共存的情形，只會有一個死亡，另一個存活的狀
況。

關鍵字

兩掠食者-一被掠食者 ； 食物模型的動態行為

並列摘要

In the work, we consider the two-predator-one prey models with Holling type II functional response. First, we show that the model is dissipative and the existence, local stability of all boundary equilibrium are clarifi ed in R3 with some suitable conditions. Then it is verifi ed that the positive equilibrium does not exist generically which is the so-called Competitive Exclusion Principle. Moreover, we obtain a classifi cation of parameter space to clarify all local dynamics of the model and two global extinction results are showed analytically. Finally, numerical simulations are presented for all regions of parameter space of our classifi cation.

並列關鍵字

Two-Predators-One-Prey Model ； Food Web Models ； Holling-type II

參考文獻

[1] K. S. Cheng. Uniqueness of a limit cycle for a predator-prey system. SIAM Journal on Mathematical Analysis, 12(4):541-548, 1981.

[2] G. Hardin. The Competitive Exclusion Principle. Science, 131:1292-1297, 1960.

[3] S. B. Hsu, S. P. Hubbell, and P. Waltman. A Contribution to the Theory of Competing Predators. Ecological Monographs, 48(3):337-349, 1978.

[4] S. B. Hsu, S. P. Hubbell, and P.Waltman. Competing predators. SIAM Journal on Applied Mathematics, 35(4):617-625, 1978.

[5] A. L. Koch. Competitive coexistence of two predators utilizing the same prey under constant environmental conditions. Journal of Theoretical Biol-ogy, 44(2):387-395, 1974.