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系統識別號 U0002-2707202200194600
DOI 10.6846/TKU.2022.00784
論文名稱(中文) 比率相關Holling III型捕食者-獵物模型的數學分析
論文名稱(英文) Mathematical Analysis of Ratio Dependent Predator-Prey Models with Holling Type III Functional Response
第三語言論文名稱
校院名稱 淡江大學
系所名稱(中文) 數學學系數學與數據科學碩士班
系所名稱(英文) Master's Program, Department of Mathematics
外國學位學校名稱
外國學位學院名稱
外國學位研究所名稱
學年度 110
學期 2
出版年 111
研究生(中文) 汪楷勛
研究生(英文) Kai-Hsun Wang
學號 608190160
學位類別 碩士
語言別 英文
第二語言別
口試日期 2022-07-13
論文頁數 10頁
口試委員 指導教授 - 楊定揮(tinghuiy@gmail.com)
口試委員 - 林建仲
口試委員 - 鄭凱仁
關鍵字(中) 動力系統
生物數學
關鍵字(英) Dynamics System
Mathematical Biology
Ratio Dependent Models
第三語言關鍵字
學科別分類
中文摘要
在這項工作中,我們考慮了比率相關 Holling III 型捕食者-獵物模型,分析了該生態系統邊界平衡點及正平衡點的穩定性,最後詳細討論並給出了一些生物學解釋。
英文摘要
In this work, we consider Ratio Dependent Predator-Prey Models with Holling Type III and analysis the stabilities of boundary equilibria and positive equilibrium. Finally, a brief discussion and some biological interpretations are given.
第三語言摘要
論文目次
目錄

1.	Introduction	1
2.	Preliminary 	3
3.	Main Results 	7
4.	Conclusion, Remarks and Biological Implications 	9
5.	References	10
參考文獻
References
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an abstraction that works. Ecology, 76:995–1004, 1995.
[2] R. Arditi, A. A. Berryman, The biological paradox, in Ecology and
Evolution. 6:32, 1991.
[3] R. Arditi and L. R. Ginzburg. Coupling in Predator-Prey Dynamics:
Ratio-Dependenc. Journal of Theoretical Biology, 139:311–326, 1989.
[4] R. Arditi, L. R. Ginzburg, H. R. Akcakaya. Variation in plankton densities among lakes: a case for ratio-dependent models, American Natrualist,
138:1287-1296 , 1991.
[5] R Arditi, N. Perrin and H. Saiah, Functional responses and heterogeneities: an experimental test with cladocerans, Oikos, 60:69-75, 1991.
[6] K. S. Chêng. Uniqueness of a limit cycle for a predator-prey system.
SIAM Journal on Mathematical Analysis, 12(4):541–548, 1981.
[7] C. Cosner, D. L. DeAngelis, J. S. Ault, D. B. Olson, Efects of spatial
grouping on the functional response of predators. Theoretical Population
Biololgy, 56:65–75, 1999.
[8] H. I. Freedman and R. M. Mathsen Persistence in predator-prey systems with ratio-dependent predator infuence, Bulletin of Mathematical
Biology, 55(4):817-827, 1993.
[9] X. Wang, M. Peng, X. Liu. Stability and Hopf bifurcation analysis of a
ratio-dependent predator–prey model with two time delays and Holling
type III functional response. Applied Mathematics and Computation,
268:496–508, 2015.
[10] Edoardo Beretta, Y. Kuang. Global analysis in some delayed ratiodependent predator-prey systems. Nonlinear Analysis, Theory, Method
& Application, 32(3):381–408, 1998.
[11] I. Hanski, The functional response of predator: worries about scale,
Tree, 6:141-142, 1991.
[12] Sze-Bi Hsu, Tzy-Wei Hwang. Yang-Kuang. Global analysis of the
Michaelis-Menten-type ratio-dependent predator-prey system. Journal
of Mathematical Biology, 42:489–506, 2001.
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