一掠食者-兩被掠食者食物網模型的動態行為研究

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

王靜雯(Ching-Wen Wang)

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.2013.00045

摘要

在這項研究中，我們考慮一掠食者-兩被掠食者模型依據Holling type II功能性反應且兩被掠食者之間不存在競爭關係。首先建立有界且有正解的初始條件，然後證明所有的邊界平衡點的存在性和穩定性在三維中。此外，我們利用掠食者的死亡率푑作為參數，分類我們的動態系統(1.2)，以及正平衡點存在性和穩定性的分析，最後利用我們的分類，進行一些數值模擬。

關鍵字

食物鏈 ； Holling法則 ； 一掠食者-兩被掠食者

並列摘要

In this work, we consider the one-predator-two-prey models with Holling type II functional response without competition between the two renewable base resource. We first establish the boundedness and positivity of solution with positive initial conditions. Then the existence and local stability of all boundary equilibria are clarified in ℝ3. Moreover, we use the death rate of predator 푑 as a parameter to classify the dynamics of system (1.2) as well as the existence and local stability of positive equilibrium. Finally, some numerical simulations are performed for each region of our classification.

並列關鍵字

Food Web Models ； Holling type II ； One-Predator-Two-Prey

參考文獻

[1] K. S. Ch^eng. Uniqueness of a limit cycle for a predator-prey system. SIAM

Journal on Mathematical Analysis, 12(4):541{548, 1981.

[2] N. F. Cramer and R. M. May. Interspeci c competition, predation and species

[5] S. Gakkhar and R. K. Naji. Existence of chaos in two-prey, one-predator

[6] M. E. Gilpin. Spiral Chaos in a Predator-Prey Model. The American Natu-