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研究生:龔一鴻
研究生(外文):Yi-Hung Kung
論文名稱:關於兩個物種對於三個相配資源競爭的數學模型
論文名稱(外文):On a Mathematical Model of Two Species Competing for Three Complementary Resources
指導教授:許世壁許世壁引用關係
指導教授(外文):Sze-Bi Hsu
學位類別:碩士
校院名稱:國立清華大學
系所名稱:數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:29
中文關鍵詞:競爭模型
外文關鍵詞:Competition Model
相關次數:
  • 被引用被引用:0
  • 點閱點閱:183
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  • 下載下載:23
  • 收藏至我的研究室書目清單書目收藏:2
本篇論文主要是在探討關於兩個物種對於三個相配資源競爭的數學模型,首先,我們會呈現一些初步的結果,顯示此一生物數學模型的行為,與我們對於生物問題的直覺是相契合的,並且將此五維度的微分方程系統降階到一個二維度的微分方程系統,然後針對這兩個物種對於此三個相配資源競爭的優劣關係,進行數學上的分析,最後我們就此分析結果去探討他們的生物意義。

This paper concerns the exploitative competition of two species for three complementary resources in a chemostat. The predicted biological conditions which should give rise to each of the possible competitive outcomes are presented in detail and analyzed globally under the different assumptions on the break-even concentrations for each nutrient. We also state some preliminary results and reduce the system of five differential equations to a system of two differential equations by using the theory of asymptotically autonomous systems.

1.Introduction..............................................1
2.The Model.................................................2
3.Preliminary Results.......................................3
4.Rest Points of Omega and Their Local Stability............7
5.Global Analysis of the Limiting System...................10
6.Discussion...............................................27
References.................................................28

(1)J. Huisman and F.J. Weissing, "Biodiversity of plankton by
species oscillations and chaos", Nature, Vol. 402, 25, Nov.
1999, pp.407-410.
(2)J. Huisman and F.J. Weissing, "Biological conditions for
oscillations and chaos generated by mult-species
competition", Ecology, 81(10), 2001, pp.2682-2695.
(3)S.B. Hsu, S. Hubbell, and P. Waltman, "A mathematical theory
for single-nutrient competition in continuous cultures of
micro-organisms", SIAM J. Appl. Math. Vol. 32(1977), pp.366-
383.
(4)J.A. Leon and D.B. Tumpson, "Competition between two species
for two complementary or substitutable resources", J.
Theor. Bio. 50(1975), pp.185-201.
(5)S.B. Hsu, K.S. Cheng, and S.P. Hubbell, "Exploitative
competition of micro-organisms for two complementary
nutrients in continuous cultures", SIAM J. Appl. Math. Vol.
41(1981), pp.422-444.
(6)A.J. Lotka, "Elements of mathematical biology", Williams and
Wilkins, Baltimore, MD, 1925.
(7)V. Volterra, "Variations and fluctuations of the number of
individuals of animal species living together", Animal
Ecology, R.N. Chapman, ed., McGraw-Hill, New York, 1926.
(8)H.R. Thieme, "Convergence results and a Poincare'-Bendixson
trichotomy for asymptotically autonomous differential
equations", J. Math. Biol. 30, pp.755-763(1992).
(9)G.J. Butler and G.S.K. Wolkowicz, "A mathematical model of
the chemostat with a general class of functions describing
nutrient uptake", SIAM J. Appl. Math. Vol. 45(1985), pp.138-
151.
(10)S.B. Hsu, "Limiting behavior for competing species", SIAM J.
Appl. Math. Vol. 34(1978), pp.760-763.

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