淡江大學覺生紀念圖書館 (TKU Library)
進階搜尋


下載電子全文限經由淡江IP使用) 
系統識別號 U0002-1908202013350700
中文論文名稱 兩個獵物一個捕食者的全局動力學行為
英文論文名稱 Global Dynamics of Two-Preys-One-Predator models
校院名稱 淡江大學
系所名稱(中) 數學學系數學與數據科學碩士班
系所名稱(英) Master's Program, Department of Mathematics
學年度 108
學期 2
出版年 109
研究生中文姓名 楊詠智
研究生英文姓名 Yung-Chih Yang
電子信箱 sf605020304@gmail.com
學號 606190063
學位類別 碩士
語文別 英文
口試日期 2020-07-03
論文頁數 16頁
口試委員 指導教授-楊定揮
委員-林建仲
委員-鄭凱仁
中文關鍵字 動力系統  生物數學 
英文關鍵字 Dynamics system  Mathematical Biology  Two-Preys-one-Predator Double space 
學科別分類
中文摘要 我們考慮了三個物種的兩個獵物-一個捕食者-生態系統-
Lotka-Volterra類型的醫療模型。 帶兩個必備
假設,我們將所有可能性按參數歸類為六種情況-
具有七個參數的空間。 三者的全局漸近穩定性
每種情況分別顯示出平衡。 最後,簡要討論並
給出了一些生物學解釋。
英文摘要 In this work, we consider the three species two-preys-one-predator ecolog-ical models with Lotka-Volterra type functional response. With two essential assumptions, we generic classify all possibilities into six cases for the parame-ter space with seven parameters. The global asymptotically stabilities of three equilibria are showed in each case, respectively. Finally, a brief discussion and
some biological interpretations are given.
論文目次 1 Introduction 4
2 Preliminary 5
3 Dynamics of (1.1) in the R3+ 8
4 Discussions and Biological Interpretations 15
5 Reference 16
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
diversity: A comment. Journal of Theoretical Biology, 34:289{293, 1972.
[3] A. El-Gohary and A. S. Al-Ruzaiza. Chaos and adaptive control in two prey,
one predator system with nonlinear feedback. Chaos, Solitons and Fractals,
34(2):443{453, 2007.
[4] K. Fujii. Complexity-stability relationship of two-prey-one-predator species system
model: local and global stability. Journal of Theoretical Biology, 69(4):613{
623, Dec. 1977.
[5] S. Gakkhar and R. K. Naji. Existence of chaos in two-prey, one-predator system.
Chaos, Solitons and Fractals, 17(4):639{649, 2003.
14
[6] M. E. Gilpin. Spiral Chaos in a Predator-Prey Model. The American Naturalist,
113(2):306{308, 1979.
[7] A. Klebano and A. Hastings. Chaos in one-predator, two-prey models: general
results from bifurcation theory. Mathematical Biosciences, 122(2):221{233, 1994.
[8] N. Krikorian. The Volterra model for three species predator-prey systems: boundedness
and stability. Journal of Mathematical Biology, 7(2):117{132, 1979.
[9] R. K. Naji and A. T. Balasim. On the dynamical behavior of three species food
web model. Chaos, Solitons and Fractals, 34(5):1636{1648, 2007.
[10] L. Markus. Asymptotically autonomous di erential systems. In Contributions
to the theory of nonlinear oscillations, vol. 3, pages 17{29. Princeton University
Press, Princeton, N. J., 1956.
[11] R. T. Paine. Food Web Complexity and Species Diversity. The American
Naturalist, 100:65{75, 1966.
[12] J. D. Parrish and S. B. Saila. Interspeci c competition, predation and species
diversity. Journal of Theoretical Biology, 27:207{220, 1970.
[13] W. Schnabl, P. F. Stadler, C. Forst, and P. Schuster. Full Characterization of a
Strange Attractor - Chaotic Dynamics in Low-Dimensional Replicator Systems.
Physica D. Nonlinear Phenomena, 48(1):65{90, Feb. 1991.
[14] Y. Takeuchi and N. Adachi. Existence and bifurcation of stable equilibrium
in two-prey, one-predator communities. Bulletin of Mathematical Biology,
45(6):877{900, 1983.
[15] R. R. Vance. Predation and Resource Partitioning in One Predator-Two Prey
Model Communities. . The American Naturalist, 112:797{813, 1978.
[16] H.-C. Wei. Numerical Revisit to a Class of One-Predator, Two-Prey Models.
International Journal of Bifurcation and Chaos, 20(8):2521{2536, 2010.
[17] A. Yamauchi and N. Yamamura. Effects of Defense Evolution and Diet Choice on Popuation Dynamics in a One-Predator-Two-Prey System. Ecology, 86(9):2513-2524, Sept. 2005.
論文使用權限
  • 同意紙本無償授權給館內讀者為學術之目的重製使用,於2020-09-30公開。
  • 同意授權瀏覽/列印電子全文服務,於2020-09-30起公開。


  • 若您有任何疑問,請與我們聯絡!
    圖書館: 請來電 (02)2621-5656 轉 2486 或 來信